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A direct Arbitrary Lagrangian Eulerian (ALE) formulation using multi-moment finite volume method for viscous compressible flows on unstructured moving grids has been developed and presented in this paper. High-order polynomials are reconstructed over a compact mesh stencil by making use of both volume integrated average value (VIA) and point values (PV) at the vertices of mesh cells which change in time. By formulating the governing equation in ALE integral form and differential form, the computational variables, VIA and PV, are updated, respectively, by a finite volume scheme and a point-wise discretization using multi-moments (VIA and PV). A simple and efficient formulation is derived for moving mesh which satisfies the geometrical conservation law. In the computations involving moving-body, the PVs of velocity at the vertices of cells adjacent to the body surface are coincided with the motion of the body, which eliminates the numerical approximation to find the cell boundary values on the body surface in conventional finite volume method. Numerical tests are presented to verify the present method as a high-order ALE formulation for compressible flows on both stationary and moving grids.

A direct Arbitrary Lagrangian Eulerian (ALE) formulation using multi-moment finite volume method for viscous compressible flows on unstructured moving grids has been developed and presented in this paper. High-order polynomials are reconstructed over a compact mesh stencil by making use of both volume integrated average value (VIA) and point values (PV) at the vertices of mesh cells which change in time. By formulating the governing equation in ALE integral form and differential form, the computational variables, VIA and PV, are updated, respectively, by a finite volume scheme and a point-wise discretization using multi-moments (VIA and PV). A simple and efficient formulation is derived for moving mesh which satisfies the geometrical conservation law. In the computations involving moving-body, the PVs of velocity at the vertices of cells adjacent to the body surface are coincided with the motion of the body, which eliminates the numerical approximation to find the cell boundary values on the body surface in conventional finite volume method. Numerical tests are presented to verify the present method as a high-order ALE formulation for compressible flows on both stationary and moving grids. [ABSTRACT FROM AUTHOR]

In the present article, we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with an appropriate predictor−corrector method to achieve higher resolutions. The underlying finite volume scheme is conservative, and it is accurate up to the second order in space. The main novelty consists in the motion of the grid. This new dynamic aspect can be used to resolve better the areas with large solution gradients or any other special features. No interpolation procedure is employed; thus, unnecessary solution smearing is avoided, and therefore, our method enjoys excellent conservation properties. The resulting grid is completely redistributed according to the choice of the so-called monitor function. Several more or less universal choices of the monitor function are provided. Finally, the performance of the proposed algorithm is illustrated on several examples stemming from the simple linear advection to the simulation of complex shallow water waves. The exact well-balanced property is proven. We believe that the techniques described in our paper can be beneficially used to model tsunami wave propagation and run-up.

An upwind-mixed finite element method with moving grids is presented to simulate quasi-nonlinear Sobolev equations. This method is constructed by two methods. The upwind method is used to approximate the the convection term of Sobolev equations, meanwhile an expanded mixed finite element method is applied to discretize the diffusion term. The scalar unknown function and the adjoint vector function can be approximated simultaneously by this method. Optimal error estimates in L2-norm are obtained for both the scalar unknown function and the adjoint vector function. Finally, numerical experiments are presented to illustrate the efficiency of this method. [ABSTRACT FROM AUTHOR]

In this paper, the circular function-based gas-kinetic scheme (CGKS), which was originally developed for simulation of flows on stationary grids, is extended to solve moving boundary problems on moving grids. Particularly, the unsteady flows through oscillating cascades are our major interests. The main idea of the CGKS is to discretize the macroscopic equations by the finite volume method while the fluxes at the cell interface are evaluated by locally reconstructing the solution of the continuous Boltzmann Bhatnagar-Gross-Krook equation. The present solver is based on the fact that the modified Boltzmann equation, which is expressed in a moving frame of reference, can recover the corresponding macroscopic equations with Chapman-Enskog expansion analysis. Different from the original Maxwellian function-based gas-kinetic scheme, in improving the computational efficiency, a simple circular function is used to describe the equilibrium state of distribution function. Considering that the concerned cascade oscillating problems belong to cases that the motion of surface boundary is known a priori, the dynamic mesh method is suitable and is adopted in the present work. In achieving the mesh deformation with high quality and efficiency, a hybrid dynamic mesh method named radial basic functions-transfinite interpolation is presented and applied for cascade geometries. For validation, several numerical test cases involving a wide range are investigated. Numerical results show that the developed CGKS on moving grids is well applied for cascade oscillating flows. And for some cases where nonlinear effects are strong, the solution accuracy could be effectively improved by using the present method. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Innovative approaches and new efficiencies in plant breeding are required to accelerate the progress of genetic improvement through selection. One such approach is the application of prognostic breeding, which is an integrated crop-improvement methodology that enables selection of plants for high crop yield potential by evaluating its two components: plant yield potential and stability of performance. Plant yield and stability are assessed concurrently in each generation by utilising the plant prognostic equation. The genetic material used for this study was 2350 F2 plants (C0) of the commercial maize hybrid Costanza. The study presents the results of the application of prognostic breeding for 6 years in two contrasting environments (A and B), starting from C0 and ending in C5. It utilises ultra-high selection pressures (1.5% to 0.5%) to isolate superior lines with crop yield comparable to Costanza, and estimates the annual genetic gain accomplished through application of this selection strategy. Application of prognostic breeding led to the isolation of superior lines whose productivity was comparable to Costanza. The productivity gap between Costanza and the best selection was reduced from 87% (C0) to 0.5% (C5) in trial 1 (environment A), from 87% (C0) to 2% (C5) in trial 2 (environment B) and from 70% (C0) to 1% (C3) in trial 3 (environment B). Genetic gain was much higher (up to 50%) in the early cycles C0-C2 of prognostic breeding and smaller in cycles C3-C5. The best lines selected were evaluated in randomised complete block trials across both environments and 2 years. Across years, the top two lines in environments A and B averaged 87% and 91% of the Costanza yield, respectively, and they had higher prolificacy (greater number of ears per plant) than Costanza. Across all cycles, the average annual genetic gain ranged from 23% to 36% in the different trials, providing evidence that selection efficiency can be significantly maximised by using this breeding strategy. [ABSTRACT FROM AUTHOR]

Consistent time integration on collocated grids for incompressible flow has been studied for static grids using the PISO method, in which the dependencies on time-step size and under-relaxation has been studied in detail. However, for moving grids a detailed description is still missing. Therefore, a step by step analysis of a time consistent fluid–structure interaction (FSI) method for incompressible flow on collocated grids is presented. The method consist of: face normal and area correction for moving grids, treatment of velocity boundary conditions for no-slip walls, time integration of structure equations and fluid force interpolation to structure. The basis of the method is the PISO method of the incompressible Navier–Stokes equations. Time consistency on static grids is shown first, after which time consistency on moving grids is described and analyzed. For moving grids consistent time integration is described in two ways: (1) constructing the face velocities from a normal and tangential component, and (2) correcting the face flux with a face normal and face area correction. For both descriptions the general formulation for the backward differencing schemes (BDF) are given and the correct behavior of the first, second and third order schemes is demonstrated by means of an academic test case (circular cavity flow). Additionally, the (force) coupling from the fluid to the structure is discussed in detail for combining a fourth order explicit Runge Kutta scheme for the structure with a BDF scheme for the fluid. Three interpolations for the fluid forces are shown, which result in either a first order or second order FSI scheme. Third order FSI is demonstrated when the third order BDF scheme is applied on both the structure and fluid equations. Also, under-relaxation for the fluid equations is considered and it is demonstrated that the order of the three BDF schemes are independent of the under-relaxation factor. Finally, the proposed method of time consistent FSI on collocated grids for incompressible flows is demonstrated by applying it to a three-dimensional flow over an elastic structure in a channel and the cylinder flap FSI benchmark case of Turek and Hron. [ABSTRACT FROM AUTHOR]

Purpose: Apreobject grid can reduce and correct scatter in cone beam computed tomography (CBCT). However, half of the signal in each projection is blocked by the grid. A synchronized moving grid (SMOG) has been proposed to acquire two complimentary projections at each gantry position and merge them into one complete projection. That approach, however, suffers from increased scanning time and the technical difficulty of accurately merging the two projections per gantry angle. Herein, the authors present a new SMOG approach which acquires a single projection per gantry angle, with complimentary grid patterns for any two adjacent projections, and use an interprojection sensor fusion (IPSF) technique to estimate the blocked signal in each projection. The method may have the additional benefit of reduced imaging dose due to the grid blocking half of the incident radiation. Methods: The IPSF considers multiple paired observations from two adjacent gantry angles as approximations of the blocked signal and uses a weighted least square regression of these observations to finally determine the blocked signal. The method was first tested with a simulated SMOG on a head phantom. The signal to noise ratio (SNR), which represents the difference of the recovered CBCT image to the original image without the SMOG, was used to evaluate the ability of the IPSF in recovering the missing signal. The IPSF approach was then tested using a Catphan phantom on a prototype SMOG assembly installed in a bench top CBCT system. Results: In the simulated SMOG experiment, the SNRs were increased from 15.1 and 12.7 dB to 35.6 and 28.9 dB comparing with a conventional interpolation method (inpainting method) for a projection and the reconstructed 3D image, respectively, suggesting that IPSF successfully recovered most of blocked signal. In the prototype SMOG experiment, the authors have successfully reconstructed a CBCT image using the IPSF-SMOG approach. The detailed geometric features in the Catphan phantom were mostly recovered according to visual evaluation. The scatter related artifacts, such as cupping artifacts, were almost completely removed. Conclusions: The IPSF-SMOG is promising in reducing scatter artifacts and improving image quality while reducing radiation dose. [ABSTRACT FROM AUTHOR]

SUMMARY We develop a second-order accurate Navier-Stokes solver based on r-adaptivity of the underlying numerical discretization. The motion of the mesh is based on the fluid velocity field; however, certain adjustments to the Lagrangian velocities are introduced to maintain quality of the mesh. The adjustments are based on the variational approach of energy minimization to redistribute grid points closer to the areas of rapid solution variation. To quantify the numerical diffusion inherent to each method, we monitor changes in the background potential energy, computation of which is based on the density field. We demonstrate on a standing interfacial gravity wave simulation how using our method of grid evolution decreases the rate of increase of the background potential energy compared with using the same advection scheme on the stationary grid. To further highlight the benefit of the proposed moving grid method, we apply it to the nonhydrostatic lock-exchange flow where the evolution of the interface is more complex than in the standing wave test case. Naive grid evolution based on the fluid velocities in the lock-exchange flow leads to grid tangling as Kelvin-Helmholtz billows develop at the interface. This is remedied by grid refinement using the variational approach. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY The Chimera technique for moving grids is used to take into account nonhomogeneous unsteady inflow conditions in the simulation of aerodynamic flows. The method is applied to simulate the transport of a large-scale vortex by a mean velocity field over a large distance, where it finally interacts with an airfoil. The Chimera approach allows one to resolve the vortex on a fine grid, whereas the unstructured background grid covering most of the computational domain can be much coarser. This method shows the same low numerical dissipation as a simulation on a globally fine grid. Several precursor tests are performed with a finite modified analytical Lamb-Oseen type vortex to study the influence of spatial and temporal resolution and the employed numerical scheme. Then, the interaction of an analytical vortex with a NACA0012 airfoil and with an ONERA-A airfoil near stall is studied. Finally, a realistic vortex is generated by a ramping airfoil and is transported on a moving Chimera block and then interacts with a two-element airfoil, which allows one to simulate a typical setup for a gust generator in aerodynamic facilities. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A Crank-Nicolson scheme based on nonconforming finite element with moving grids is discussed for a class of parabolic integro-differential equations under anisotropic meshes. The corresponding convergence analysis is presented and the error estimates are obtained by using the interpolation operator instead of the conventional elliptic projection which is an indispensable tool in the convergence analysis of traditional finite element methods in previous literature. [ABSTRACT FROM AUTHOR]

Abstract: The objective of this paper is to report on the development of a method of lines (MOL) toolbox within MATLAB, and especially, on the implementation and test of a moving grid algorithm based on the equidistribution principle. This new implementation includes various spatial approximation schemes based on finite differences and slope limiters, the choice between several monitor functions, automatic grid adaptation to the initial condition, and provides a relatively easy tuning for the non-expert user. Several issues, including the sensitivity of the numerical results to the tuning parameters, are discussed. A few test problems characterized by solutions with steep moving fronts, including the Buckley–Leverett equation and an extended Fisher–Kolmogorov equation, are investigated so as to demonstrate the algorithm and software performance. [Copyright &y& Elsevier]

Abstract: An algorithm is proposed for the computation of unsteady incompressible laminar flows involving moving boundaries using body-fitted coordinates. It is shown analytically and numerically that if the non-conservative form of equations (only suitable for incompressible flows) is utilized, a uniform flow field when substituted in the transport equations does not lead to any spurious terms. Therefore, computation of incompressible flows on moving or deforming grids with this methodology would eliminate any consideration like the geometrical conservation law. The results of the bench mark cases show that the procedure is quite robust and yields accurate results. [Copyright &y& Elsevier]

Abstract: The compressible air flow in a typical puffer chamber with moving contact between fixed electrodes has been studied using computational fluid dynamics techniques. Moving grid methods in CFD process not only plays a pivotal role in understanding the flow behavior in time domain but also helps for fixing the internals at optimal locations. A typical laboratory puffer chamber geometry has been extracted from the published literature and generated multi-block structured grid using Altair’s HyperMesh software. Flow simulation in axi-symmetry duct comprises fixed electrodes, moving contact and exit duct has been carried out with ANSYS-CFX software. It has been observed that, due to steps and curvature in the geometry, flow takes different turns from inlet and velocity distribution between fixed electrodes indicates vortex flow with turbulent eddies. CFD simulation with valve element mesh motion indicates that pressure history is significantly affected by the velocity of moving contact in the puffer chamber. The results obtained for a typical puffer chamber with the mesh motion are qualitative in nature and forms the sound basis for future design studies of electro-fluid dynamics of circuit breakers. [Copyright &y& Elsevier]

Abstract: The problem of a particle impacting on a wall, a common phenomenon in particle-laden flows in the minerals and process industries, is investigated computationally using a spectral-element method with the grid adjusting to the movement of the particle towards the wall. Remeshing is required at regular intervals to avoid problems associated with mesh distortion and the constantly reducing maximum time-step associated with integration of the non-linear convective terms of the Navier–Stokes equations. Accurate interpolation between meshes is achieved using the same high-order interpolation employed by the spectral-element flow solver. This approach allows the full flow evolution to be followed from the initial approach, through impact and afterwards as the flow relaxes. The method is applied to the generic two-dimensional and three-dimensional bluff body geometries, the circular cylinder and the sphere. The principal case reported here is that of a particle colliding normally with a wall and sticking. For the circular cylinder, non-normal collisions are also considered. The impacts are studied for moderate Reynolds numbers up to approximately 1200. A cylindrical body impacting on a wall produces two vortices from its wake that convect away from the cylinder along the wall before stalling while lifting induced wall vorticity into the main flow. The situation for a sphere impact is similar, except in this case a vortex ring is formed from the wake vorticity. Again, secondary vorticity from the wall and particle plays a role. At higher Reynolds number, the secondary vorticity tends to form a semi-annular structure encircling the primary vortex core. At even higher Reynolds numbers, the secondary annular structure fragments into semi-discrete structures, which again encircle and orbit the primary core. Vorticity fields and passive tracer particles are used to characterize the interaction of the vortical structures. The evolution of the pressure and viscous drag coefficients during a collision are provided for a typical sphere impact. For a Reynolds number greater than approximately 1000 for a sphere and 400 for a cylinder, the primary vortex core produced by the impacting body undergoes a short-wavelength instability in the azimuthal/spanwise direction. Experimental visualisation using dye carried out in water is presented to validate the predictions. [Copyright &y& Elsevier]

This paper is devoted to the five parameters nonconforming finite element schemes with moving grids for velocity-pressure mixed formulations of the nonstationary Stokes problem in 2-D. We show that this element has anisotropic behavior and derive anisotropic error estimations in some certain norms of the velocity and the pressure based on some novel techniques. Especially through careful analysis we get an interesting result on consistency error estimation, which has never been seen for mixed finite element methods in the previously literatures. [ABSTRACT FROM AUTHOR]

As application of computational fluid dynamics (CFD) technology grows from the simulation of flows around fixed and rigid obstacles to the prediction of flows past flexible and/or moving bodies, interest in CFD on dynamic meshes increases. This paper reviews some of the theoretical and computational advances made in this area, highlights sample applications they have enabled in aeroelasticity and multidisciplinary optimization, and concludes with a brief discussion of a specific barrier to progress. [ABSTRACT FROM AUTHOR]

Abstract: We study the problem of deforming unstructured grids using pseudo-structural lumped-parameter systems. A basic network of edge springs is complemented with an additional set of linear springs that oppose element collapsing. This is here achieved by confining each mesh vertex to its ball, through linear springs that are attached to the vertex and to its projections on the ball entities. The resulting linear pseudo-structural problem can be solved efficiently with an iterative method. The proposed procedures are compared with a revisited version of the torsional spring method with the help of two and three-dimensional example problems. [Copyright &y& Elsevier]

Abstract: A version of the WAVEWATCH III wave model featuring a continuously moving spatial grid is presented. The new model option/version is intended for research into wind waves generated by tropical cyclones in deep water away from the coast. The main advantage of such an approach is that the cyclones can be modeled with spatial grids that cover much smaller areas than conventional fixed grids, making model runs with high spatial resolution more economically feasible. The model modifications necessary are fairly trivial. Most complications occur due to the Garden Sprinkler effect (GSE) and methods used to mitigate it. The basic testing of the model is performed using idealized wind fields consisting of a Rankine vortex. The model is also applied to hurricane Lili in the Gulf of Mexico in October 2002. The latter application shows that the moving grid approach provides a natural way to deal with hurricane wind fields that have a high-resolution in space, but a low resolution in time. Although the new model version is originally intended for tropical cyclones, it is suitable for high-resolution modeling of waves due to any moving weather pattern. [Copyright &y& Elsevier]

Two methodologies for designing an arbitrary Lagrangian–Eulerian (ALE) time-integrator for the semi-discrete Navier–Stokes equations are reviewed. Each methodology consists of a different mathematical framework for extending to moving grids a numerical scheme originally developed for computational fluid dynamics (CFD) on fixed grids, while preserving its formal order of time-accuracy established on fixed grids. Given a favorite scheme for the solution on fixed grids of the discrete Navier–Stokes equations, each of these two mathematical frameworks can generate multiple ALE extensions that share the same order of time-accuracy on moving grids. Typically, only a subset of these ALE schemes satisfy their respective discrete geometric conservation laws (DGCLs). Next, using a nonlinear scalar conservation law (NSCL) as a model problem, it is proved that satisfying the corresponding DGCL is a necessary condition for any ALE scheme to preserve on moving grids the nonlinear stability properties of its fixed-grid counterpart. Using the same NSCL, it is also proved that for the ALE extension of the second-order time-accurate trapezoidal rule, the DGCL requirement is a necessary as well as sufficient condition for nonlinear stability on moving grids. Hence, each of the two mathematical frameworks described in this paper combined with the DGCL test provides a general methodology for designing a robust ALE time-integrator for the solution of unsteady flow problems on dynamic meshes. As an example, the ALE extension of the popular three-point backward difference scheme is discussed in details. The corresponding theoretical results are illustrated with its application to the solution of various unsteady flow problems arising from the vibrations of the AGARD Wing 445.6 as well as a complete F-16 configuration in transonic airstreams. [Copyright &y& Elsevier]

In this paper we discuss a two-dimensional adaptive grid method that is based on a tensor-product approach. Adaptive grids are a commonly used tool for increasing the accuracy and reducing computational costs when solving both partial differential equations (PDEs) and ordinary differential equations. A traditional and widely used form of adaptivity is the concept of equidistribution, which is well-defined and well-understood in one space dimension. The extension of the equidistribution principle to two or three space dimensions, however, is far from trivial and has been the subject of investigation of many researchers during the last decade. Besides the nonsingularity of the transformation that defines the nonuniform adaptive grid, the smoothness of the grid (or transformation) plays an important role as well. We will analyse these properties and illustrate their importance with numerical experiments for a set of time-dependent PDE models with steep moving pulses, fronts, and boundary layers. [Copyright &y& Elsevier]

In this paper, a time-dependant calculation of flow in a lobe pump is presented. Calculations are performed using the arbitrary Lagrangean Eulerean (ALE) method. A grid manipulator is needed to move the nodes between time steps. The used grid manipulator is based on the pseudo-force idea. This means that each node is fictitiously connected with its 8 neighbours via fictitious springs. The equilibrium of the resulting pseudo spring forces defines the altered position of the nodes. The grid manipulator was coupled with a commercial flow solver and the whole was tested on the flow through a three-lobe lobe pump. Results were obtained for a rotational speed of 460 rpm and incompressible silicon oil as fluid. [ABSTRACT FROM AUTHOR]

We consider the solution of inviscid as well as viscous unsteady flow problems with moving boundaries by the arbitrary Lagrangian–Eulerian (ALE) method. We present two computational approaches for achieving formal second-order time-accuracy on moving grids. The first approach is based on flux time-averaging, and the second one on mesh configuration time-averaging. In both cases, we prove that formally second-order time-accurate ALE schemes can be designed. We illustrate our theoretical findings and highlight their impact on practice with the solution of inviscid as well as viscous, unsteady, nonlinear flow problems associated with the AGARD Wing 445.6 and a complete F-16 configuration. [Copyright &y& Elsevier]

In this paper a moving finite element method is developed to solve time dependent problems in two space dimensions. In this formulation the solution is approximated by a piecewise polynomial of high degree on a hexagonally connected triangular mesh. Special treatment, such as the way of calculating the integrals involving second spatial derivatives and the way of preventing singularities are introduced and discussed. Numerical experiments are employed to illustrate the relationship between the nodes movements and the choice of penalty constants as well as to test the accuracy and efficiency of the proposed method. [Copyright &y& Elsevier]

We present a three-dimensional spring analogy method for updating the position of unstructured dynamic meshes that features torsional springs for controlling the arbitrary motion of the grid points. We show that these torsional springs can be designed to prohibit the interpenetration of neighboring tetrahedra, and therefore to provide the method of spring analogy with the robustness needed for enlarging its range of applications. We illustrate the proposed spring analogy method with the solution of three-dimensional flow problems with complex moving boundaries, and where the unstructured meshes undergo significant deformations. We highlight the advantages of this method with respect to robustness and mesh quality, and address its computational performance. [Copyright &y& Elsevier]

An unsteady Navier-Stokes (N-S) solver based on the method of operator splitting and artificial compressibility has been studied for the moving boundary problem to simulate blood flow through a compliant vessel. Galerkin finite element analysis is used to discretize the governing equations. The model has been applied to a time-varying computational domain (two-dimensional tube) as a test case for validation. Consideration has been given to retaining the space conservation property. The same code is then applied to a hypothetical critical high-pressure gradient over a short length of blood vessel based on the spring and dashpot model. The governing equation for the blood vessel is based on two-dimensional dynamic thin-shell theory that takes into account the curvature of the stenotic portion of the vessel. Progressing the solution towards steady state is considered, as the main objective is to show the viability of the current technique for fluid/structure interactions. Preliminary results of the wall velocity and displacement based on steady state prediction agree well with data in the literature. Results, such as the streamlines, wall pressures and wall shear stress depict the possible progression of arterial disease. [ABSTRACT FROM AUTHOR]

A Laplacian smoothing of the mesh velocities with variable diffusivity based on the distance from moving bodies is introduced. This variable diffusivity enforces a more uniform mesh velocity in the region close to the moving bodies. Given that in most applications these are regions where small elements are located, the new procedure decreases element distortion considerably, reducing the need for local or global remeshing, and in some cases avoiding it altogether. [ABSTRACT FROM AUTHOR]

In the present article, we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with an appropriate predictor–corrector method to achieve higher resolutions. The underlying finite volume scheme is conservative, and it is accurate up to the second order in space. The main novelty consists in the motion of the grid. This new dynamic aspect can be used to resolve better the areas with large solution gradients or any other special features. No interpolation procedure is employed; thus, unnecessary solution smearing is avoided, and therefore, our method enjoys excellent conservation properties. The resulting grid is completely redistributed according to the choice of the so-called monitor function. Several more or less universal choices of the monitor function are provided. Finally, the performance of the proposed algorithm is illustrated on several examples stemming from the simple linear advection to the simulation of complex shallow water waves. The exact well-balanced property is proven. We believe that the techniques described in our paper can be beneficially used to model tsunami wave propagation and run-up. [ABSTRACT FROM AUTHOR]

Prognostic breeding is a crop improvement methodology that utilizes prognostic equations to enable concurrent selection for plant yield potential and stability of performance. There is a necessity for plant breeders to accurately phenotype plants in the field and select effectively for high and stable crop yield in the absence of the confounding effects of competition. Prognostic breeding accomplishes this goal by evaluating plants for (i) plant yield potential and (ii) plant stability, in the same generation. The plant yield index, stability index and the plant prognostic equation are the main criteria used for the selection of the best plants and the best entries grown in honeycomb designs. The construction of honeycomb designs and analysis of experimental data in prognostic breeding necessitate the development of a computer program to ensure accurate measurement of the prognostic equations. The objective of this paper is to introduce the Prognostic Breeding Application JMP Add-In, a program for constructing honeycomb designs and analyzing data for the efficient selection of superior plants and lines. The program displays powerful controls, allowing the user to create maps of any honeycomb design and visualize the selected plants in the field. Multi-year soybean data are used to demonstrate key features and graphic views of the most important steps. [ABSTRACT FROM AUTHOR]