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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&ndash, 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.

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.

Accepted: 2016-03-24, 資料番号: SA1160148000

In this paper, we propose a hybrid lattice Boltzmann method (HLBM) for solving fluid-structure interaction problems. The proposed numerical approach is applied to model the flow induced by a vibrating thin lamina submerged in a viscous quiescent fluid. The hydrodynamic force exerted by the fluid on the solid body is described by means of a complex hydrodynamic function, whose real and imaginary parts are determined via parametric analysis. Numerical results are validated by comparison with those from other numerical as well as experimental works available in the literature. The proposed hybrid approach enhances the capability of lattice Boltzmann methods to solve fluid dynamic problems involving moving geometries., 16 pages, 6 figures

El modelo numérico CAFFA3D.MBRI se enmarca en el área de mecánica de los fluidos computacional y su aplicabilidad abarca el estudio de flujos tridimensionales viscosos, turbulentos, incompresibles, con transporte de escalares o con superficie libre, entre muchos otros. Es una implementación del Método de Volúmenes Finitos que utiliza mallas curvilíneas y estructuradas por bloques, que permite dividir la tarea realizando el cálculo en paralelo bajo el estándar MPI. En el presente trabajo se desarrollan nuevas extensiones del código, que permiten su aplicación a situaciones que involucren la interacción entre un cuerpo rígido, de forma arbitraria, y un flujo en el que se encuentra inmerso. La presencia del cuerpo se realiza adaptando implementaciones del Método de Condiciones de Borde Inmersas (IBM) y su movimiento de traslación y rotación se calcula con las ecuaciones de la mecánica clásica, discretizadas bajo un esquema leapfrog con sobre-relajación. El cálculo preciso de la fuerza y momento de fuerza de interacción sólido-fluido requiere la utilización de mallas muy finas, que conlleva un elevado costo computacional. Para obtener un cálculo preciso y con un costo computacional moderado, en este trabajo se adapta una implementación previa de la técnica de mallas anidadas para que se muevan de manera solidaria al cuerpo. Esto permite tener en todo momento un refinamiento local de malla en la cercanía del rígido. Además, la técnica completa se implementó para el caso en que intervienen varios rígidos de forma arbitraria. Se aplicó el código generado a diferentes problemas físicos para su validación y para el análisis de su capacidad. Los resultados para el análisis en dos (tres) dimensiones de la caída, bajo la acción de la gravedad, de un círculo (esfera) inmerso en un fluido newtoniano confinado en un recipiente están en excelente concordancia con referencias previas. Además, se modeló la fuerza de choque entre dos cuerpos para analizar el caso de la caída en dos (tres) dimensiones de dos círculos (esferas). Se obtuvieron excelentes resultados y se logró reproducir el fenómeno de drafting, kissing and tumbling (DKT). Para mostrar la capacidad del código frente a problemas de interés tecnológico, se aplicó el modelo al problema de resuspensión de sedimentos para el caso en dos dimensiones de un sedimento circular que es removido de la pared inferior del dominio por un flujo de Poiseuille entre dos paredes horizontales paralelas. El método desarrollado permitirá estudiar situaciones en un amplio rango de escalas. Desde escalas biológicas, como la propagación de glóbulos rojos en el torrente sanguíneo, hasta grandes escalas, por ejemplo en la resuspensión de sedimentos en el fondo de un río o el movimiento de un aerogenerador cuando interactúa con un viento durante la generación de energía eólica. The so called caffa3d.mbri is a flow solver which scope includes the study of viscous, turbulent, incompressible, or transporting a contamin ant flows, to mention some. It is an implementation of the finite volume method and uses curvilinear, block-structured grids, allowing the code parallelization using the MPI library. In this work we continue with the development of the code, in order to expand its applicability to cases involving the interaction between a rigid body of given shape and the flow in which it is immersed. The body is represented by means of the immersed boundary method and its motion and rotation are obtained by solving the equations from classical mechanics, using an over-relaxed leapfrog time scheme. A very accurate force and moment calculation, as a result of rigid-flow interaction, resulting from the body-flow interaction, requires the use of fine meshes, leading to a great numerical effort. In order to obtain an accurate solution and save numerical effort, in this work we adapted a previous implementation of the nesting technique, which gives the solver the capability of overlapping fine meshes on the volume occupied by the rigid, at every time step of the simulation. These meshes can also move and rotate following the body state, so that we get mesh refinement only in its vicinity, that is, where it is needed. Moreover, the described technique is also extended for cases involving many bodies. The solver is applied to different physical problems for its validation and to test its real capabilities. Among them, we studied the falling, due to the gravity, of a circle (sphere) immersed in a newtonian fluid in a container, in two (three) dimensions, obtaing results which are excellent agreement with previous works. In the second study, we considered the two (three) dimensional problem concerning two circles (spheres) falling immersed in a newtonian fluid contained in a closed container. For that purpose, we added the calculation for the collision force between the bodies. The problem was solved properly and the typical drafting, kissing and tumbling phenomenon (DKT) was observed. Finally, we apply the solver for simulating a problem concerning the resuspension of sediments, which has great technological interest. It consists on a two dimensional Poiseuille flow between two horizontal walls, that causes the remotion of a circular body initially at rest over the bottom wall and then advected by the flow. The new features incorporated to the code made it capable of studying real world applications where the interaction between fluid an rigid bodies is present, in a wide range of scales. From the transport of red blood cells by the bloodstream, or the resuspension of sediments at the bottom of the riverflow, to the motion of wind turbines during the generation of wind power.

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.

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.

The next generation of semiconductor process and device modeling codes will require 3-D mesh capabilities including moving volume and surface grids, adaptive mesh refinement and adaptive mesh smoothing. To illustrate the value of these techniques, a time dependent process simulation model was constructed using analytic functions to return time dependent dopant concentration and time dependent SiO2 volume and surface velocities. Adaptive mesh refinement and adaptive mesh smoothing techniques were used to resolve the moving boron dopant diffusion front in the Si substrate. The adaptive mesh smoothing technique involves minimizing the L2 norm of the gradient of the error between the true dopant concentration and the piecewise linear approximation over the tetrahedral mesh thus assuring that the mesh is optimal for representing evolving solution gradients. Also implemented is constrained boundary smoothing, wherein the moving SiO2/Si interface is represented by moving nodes that correctly track the interface motion, and which use their remaining degrees of freedom to minimize the aforementioned error norm. Thus, optimal tetrahedral shape and alignment is obtained even in the neighborhood of a moving boundary. If desired, a topological “reconnection” step maintains a Delaunay mesh at all times. The combination of adaptive refinement, adaptive smoothing, and mesh reconnection gives excellent front tracking, feature resolution, and grid quality for finite volume/finite element computation.

The Los Alamos 3D grid toolbox handles grid maintenance chores and provides access to a sophisticated set of optimization algorithms for unstructured grids. The application of these tools to semiconductor problems is illustrated in three examples: grain growth, topographic deposition and electrostatics. These examples demonstrate adaptive smoothing, front tracking, and automatic, adaptive refinement/derefinement.

There is an increasing interest in flow simulations in configurations where parts are moving relatively to each other. A general approach to this problem is the use of overlapping grids, often called Chimera-technique. An incompressible flow solver based on a projection scheme with a fast multi-grid method for the pressure correction equation requires an implicit coupling between the grids on all levels of the multi-grid hierarchy in order to retain the good convergence properties. The efficient implementation of the overlapping grid technique in the DLR THETA code and its validation are presented in this chapter.

We examine a number of adaptive space mesh routines which were designed to provide accurate numerical approximations to the solutions of parabolic partial differential equations in one space dimension. Both static and dynamic regridding techniques are considered, and in numerical experiments, we compare their relative performances by measuring a range of statistics including accuracy and cpu when applied to approximate the solutions of a set of representative test problems.

A set of algorithms building a program package for the generation of twoandthree-dimensional unstructured/hybrid grids around complex geometrieshas been developed. The unstructured part of the grid generator is based on the advancing frontalgorithm. Tetrahedra of variable size, as well as directionally stretched tetrahedracan be generated by specification of a proper background grid, initiallygenerated by a Delaunay algorithm. A marching layer prismatic grid generation algorithm has been developedfor the generation of grids for viscous flows. The algorithm is able to handleregions of narrow gaps, as well as concave regions. The body surface is describedby a triangular unstructured surface grid. The subsequent grid layers in theprismatic grid are marched away from the body by an algebraic procedurecombined with an optimization procedure, resulting in a semi-structured gridof prismatic cells. Adaptive computations using remeshing have been done with use of a gradientsensor. Several key-variables can be monitored simultaneously. The sensorindicates that only the key-variables with the largest gradients give a substantialcontribution to the sensor. The sensor gives directionally stretched grids. An algorithm for the surface definition of curved surfaces using a biharmonicequation has been developed. This representation of the surface canbe used both for projection of the new surface nodes in h-refinement, and theinitial generation of the surface grid. For unsteady flows an algorithm has been developed for the deformationof hybrid grids, based on the solution of the biharmonic equation for the deformationfield. The main advantage of the grid deformation algorithm is that itcan handle large deformations. It also produces a smooth deformation distributionfor cells which are very skewed or stretched. This is necessary in orderto handle the very thin cells in the prismatic layers. The algorithms have been applied to complex three-dimensional geometries,and the influence of the grid quality on the accuracy for a finite volumeflow solver has been studied for some simpler generic geometries. QC 20100812

A Computational Fluid Dynamics analysis is undertaken to predict static- and dynamic-aerodynamic coefficients for re-entry vehicles. To determine the dynamic behavior of flying vehicles, here is presented a strategy based on the DLR CFD-TAU code with integrated flight mechanics equations in combination with a novel Chimera-Technique. The new Chimera strategy provides also a way to perform grid independent studies when using hybrid meshes. The present results demonstrate the potential of the technique as a major step to remove the classical illness of the force oscillation approach for the prediction of dynamic derivatives on re-entry vehicles.

Im Rahmen dieser Arbeit wird eine neuartige Blutpumpe für ein Herzunterstützungssystem entwickelt, die ohne Lager betrieben werden kann. Dabei schwebt der Rotor frei in einem Gehäuse und wird nur durch hydrodynamische und magnetische Kräfte stabilisiert. Mittels stationärer Strömungssimulationen wird ein erster Prototyp der Blutpumpe entworfen und im Hinblick auf hydraulische Effizienz und hohe hydrodynamische Kräfte zur Rotorstabilisierung optimiert. Außerdem werden die Fluid-Struktur Wechselwirkungen zwischen dem Fördermedium Blut und dem Rotor zeitecht auf bewegten Rechengittern simuliert. Der Vergleich von numerisch und experimentell gewonnenen Ergebnissen zeigt eine gute Übereinstimmung. Um das Ausmaß an Blutschädigung durch ein virtuelles Blutpumpendesign beurteilen zu können, wird ein Verfahren vorgestellt, mit dem aus den Ergebnisdaten numerischer Strömungssimulationen die Belastung von Blutzellen auf dem Weg durch die Pumpe ermittelt werden kann. Der Vergleich der im Rahmen dieser Arbeit entworfenen Pumpe mit bestehenden Systemen zeigt, daß die Pumpe sehr blutschonend arbeitet. In this thesis a new implantable centrifugal blood pump for an artificial heart system is presented. The rotor of this seal-less pump is suspended by hydrodynamic and magnetic forces. By means of stationary computational fluid dynamics simulations, a first prototype of the pump is designed and optimized in terms of high hydraulic efficiency and large hydrodynamic forces for the stabilization of the rotor. Furthermore, the transient Fluid-Structure interactions between the blood and the rotor are simulated employing moving grids. The results obtained from numerical simulations are compared to data from measurements and show good agreement. In order to determine the amount of blood damage by a virtual design of a blood pump, a method is presented where the damage of the red blood cells can be calculated from the results of numerical flow simulations. A comparision of the new device with existing pumps shows an excellent performance of the pump in terms of blood damage.

International audience; 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.

In this paper the moving-nite-element method (MFE) is used to solve the heat equation, with an articial time component, to give a non-uniform (steady-state) grid that is adapted to a given prole. It is known from theory and experiments that MFE, applied to parabolic PDEs, gives adaptive grids which satisfy an equidistribution type law. This property is used to create non-uniform nite-element grids that are dictated by second-order derivatives of the solution. The proposed procedure could be used to create an initial grid for MFE itself, to dene a regridding strategy for MFE in case of a distorted grid, or to prescribe a new adaptive grid method where the heat quation is used as a "monitor function".

In this paper the moving-nite-element method (MFE) is used to solve the heat equation, with an articial time component, to give a non-uniform (steady-state) grid that is adapted to a given prole. It is known from theory and experiments that MFE, applied to parabolic PDEs, gives adaptive grids which satisfy an equidistribution type law. This property is used to create non-uniform nite-element grids that are dictated by second-order derivatives of the solution. The proposed procedure could be used to create an initial grid for MFE itself, to dene a regridding strategy for MFE in case of a distorted grid, or to prescribe a new adaptive grid method where the heat quation is used as a "monitor function".