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The fractional step method is used to solve the ionization equations for electron-ion plasma containing neutrals in relation to processes in stationary plasma thrusters (SPT). The method uses splitting with respect to physical processes: the evolution of plasma is represented as a superposition of pure transport in an external field in phase space with subsequent ionization. The transport is calculated using the macroparticle method. The ionization process in the case of plane symmetry is calculated using explicit analytical formulas. The resulting formulas of the fractional step method are compared with the numerical solution of the plasma evolution equation using the known physical model of ionization. [ABSTRACT FROM AUTHOR]

Fast flow simulation is imperative in the design of pulsating ventilation, which is potentially efficient in indoor air contaminant removal. The execution of the conventional CFD method requires considerable amount of computational resources. In this study, five different numerical schemes were proposed based on fast fluid dynamics (FFD) and fractional step (FS) methods, and were evaluated to achieve quick simulation of airflow/contaminant dispersion. One of these numerical schemes was identified with the best overall computing efficiency for investigating the performance of pulsating ventilation. With this numerical scheme at hand, the air contaminant removal effectiveness of different ventilation types was evaluated. Two kinds of pulsating ventilation and one kind of steady ventilation were tested upon a benchmark isothermal mixing chamber. The effect of adjusting supply velocity parameters on the ventilation performance was also investigated. CO2 concentration, airflow pattern, and vortex structure of different ventilation types were illustrated and analyzed. The results reveal that the FS method is more suitable for transient simulation of wall-bounded indoor airflow than the FFD method, and 34%–51% of computing time could be saved compared to the conventional CFD method. Regarding the choice of ventilation type, steady ventilation might result in short-circuit airflow and stagnant zones; alternatively, pulsating ventilation has greater potential in air contaminant removal due to its ever-changing vortex structure. [ABSTRACT FROM AUTHOR]

It is generally accepted that the central differences scheme with a stabilizing correction for the transport equation in the 3D case is conditionally stable. This article shows that, strictly speaking, this scheme is absolutely unstable. However, the region of unstable harmonics in the wave vector space and their increments quickly tend to zero as the Courant parameter tends to zero, which makes it possible to successfully use this scheme. Therefore, it is more correct to talk about the practically conditional stability of this scheme. [ABSTRACT FROM AUTHOR]

The paper concerns a nonlinear second-order system of coupled PDEs, having the principal part in divergence form and subject to in-homogeneous dynamic boundary conditions, for both θ (t , x) and φ (t , x) . Two main topics are addressed here, as follows. First, under a certain hypothesis on the input data, f 1 , f 2 , w 1 , w 2 , α , ξ , θ 0 , α 0 , φ 0 , and ξ 0 , we prove the well-posedness of a solution θ , α , φ , ξ , which is θ (t , x) , α (t , x) ∈ W p 1 , 2 (Q) × W p 1 , 2 (Σ) , φ (t , x) , ξ (t , x) ∈ W ν 1 , 2 (Q) × W p 1 , 2 (Σ) , ν = min { q , μ } . According to the new formulation of the problem, we extend the previous results, allowing the new mathematical model to be even more complete to describe the diversity of physical phenomena to which it can be applied: interface problems, image analysis, epidemics, etc. The main goal of the present paper is to develop an iterative scheme of fractional-step type in order to approximate the unique solution to the nonlinear second-order system. The convergence result is established for the new numerical method, and on the basis of this approach, a conceptual algorithm, alg-frac_sec-ord_u+varphi_dbc, is elaborated. The benefit brought by such a method consists of simplifying the computations so that the time required to approximate the solutions decreases significantly. Some conclusions are given as well as new research topics for the future. [ABSTRACT FROM AUTHOR]

In the present study, a fractional three-step P2P1 finite element method (FEM) for solving the unsteady incompressible Navier-Stokes equations, which is a variation of P1P1 four-step splitting FEM [1], was compared with conventional one-step time-integration schemes in terms of the CPU time and convergence characteristics of an iterative solver by the solution of some benchmark problems. One-step time-integration schemes were temporarily discretized by either the Crank-Nicolson or the Adams-Bashforth method. Fractional three-step P2P1 FEM consists of three steps: a non-linear momentum equation with the pressure in the previous time step is solved to obtain an intermediate velocity field by the Crank-Nicolson method in the first step and another intermediate velocity field is calculated using the pressure in the previous time step in the second step, and a divergence-free constraint is imposed in the last step to update the pressure field, in which a symmetric saddle-point type matrix (SPTM) is solved. It was shown that the fractional three-step method is more efficient than one-step time-integration schemes because a symmetric SPTM is assembled only once during the entire computation and solved once at each time-step; further, the cost of solving the nonlinear momentum equation in a fully-implicit manner is relatively low. Furthermore, the proposed method was found to be more stable than one-step time-integration schemes as it provided stable solutions at higher CFL numbers. [ABSTRACT FROM AUTHOR]

This paper is mainly concerned with the motion of an incompressible fluid in a slowly rotating spherical basin using the fractional step method. The algorithm is applied by splitting the three-dimensional shallow water equations into three problems each of one dimension in every direction using the Riemann invariant. The next step is the successive integration in all directions along the characteristics associated with cubic spline interpolation. It has the advantage of reducing the three-dimensional matrix problem into an equivalent one-dimensional problem, the simplicity of this algorithm makes it very suitable for parallel computers. Numerical results are represented in three-dimensional for the velocity components at different times with different Coriolis parameters. It is worthy to note that such a study has useful applications in the science of oceanography. [ABSTRACT FROM AUTHOR]

This article deals with 2D singularly perturbed parabolic delay differential equations. First, we apply implicit fractional Euler method for discretizing the derivative with respect to time and then we apply upwind finite difference method with bilinear interpolation to the locally one-dimensional problems with space shift. It is proved that the present finite difference method is almost first-order convergence in time and spatial directions. Numerical examples are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

• A magnetic field coupling FSLB method is proposed to simulate multiphase flows. • The macroscopic governing equations can be fully recovered in second-order accuracy. • We successfully perform the first rigorous numerical simulation on Rosensweig instability. • The velocity of falling ferrofluid droplet is accelerated by an opposite magnetic field. In the present study, a magnetic field coupling fractional step lattice Boltzmann (FSLB) model is proposed to simulate the complex interfacial behaviors in magnetic multiphase flows with severe interface deformation and large density ratio, which can be recovered to the corresponding macroscopic governing equations with fully second-order accuracy. Since the equilibrium and the non-equilibrium terms are obtained by the Chapman-Enskog (C-E) expansion analysis, the basic idea of the present method is to predict the intermediate variables by updating the various moments of equilibrium distribution functions first, and then correct the physical variables by updating the various moments of non-equilibrium distribution functions. Besides, the present magnetic field coupling FSLB method does not need the evolution of distribution functions compared to the existing LB methods. The present method inherits the excellent performance from the conventional LB method and the relatively better numerical stability from the matured fractional-step method, which is more stable than the original LB method and more efficiency and easy-to-implement than the LB flux solver. Owing to those good properties, we successfully perform the first rigorous numerical simulation on the Rosensweig instability, which accurately captures the spikes forming at the surface of a ferrofluid under an applied magnetic field. Moreover, for the first time we numerically reproduce the falling ferrofluid droplet impacted on the solid surface. Intriguingly, our simulation results reveal that the falling velocity of the ferrofluid droplet is slightly accelerated by the elongation, although the direction of the magnetic field is opposite to that of the gravity. All the results for the interfacial behavior and the magnetic interaction highlights the comparative capability, stability, and accuracy of the present magnetic field coupling FSLB method for simulating the problems of complex fluid dynamics associated with a severe interface deformation and large density ratio in magnetic multiphase flows. [ABSTRACT FROM AUTHOR]

Two main topics are addressed in the present paper, first, a rigorous qualitative study of a second-order reaction–diffusion problem with non-linear diffusion and cubic-type reactions, as well as inhomogeneous dynamic boundary conditions. Under certain assumptions about the input data: g d (t , x) , g f r (t , x) , U 0 (x) and ζ 0 (x) , we prove the well-posedness (the existence, a priori estimates, regularity and uniqueness) of a solution in the space W p 1 , 2 (Q) × W p 1 , 2 (Σ) . Here, we extend previous results, enabling new mathematical models to be more suitable to describe the complexity of a wide class of different physical phenomena of life sciences, including moving interface problems, material sciences, digital image processing, automatic vehicle detection and tracking, the spread of an epidemic infection, semantic image segmentation including U-Net neural networks, etc. The second goal is to develop an iterative splitting scheme, corresponding to the non-linear second-order reaction–diffusion problem. Results relating to the convergence of the approximation scheme and error estimation are also established. On the basis of the proposed numerical scheme, we formulate the algorithm alg-frac_sec-ord_dbc, which represents a delicate challenge for our future works. The benefit of such a method could simplify the process of numerical computation. [ABSTRACT FROM AUTHOR]

Singularly perturbed 2D parabolic delay differential equations with the discontinuous source term and convection coefficient are taken into consideration in this paper. For the time derivative, we use the fractional implicit Euler method, followed by the fitted finite difference method with bilinear interpolation for locally one-dimensional problems. The proposed method is shown to be almost first-order convergent in the spatial direction and first-order convergent in the temporal direction. Theoretical results are illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

We present a higher-order robust numerical method for 2D singularly perturbed delay parabolic differential equation of convection-diffusion type. For the family of such type of differential equations, till now a first-order (reduced by a logarithmic term) numerical scheme is proposed. To develop a more efficient numerical scheme, first, we time-discretize the problem in such a way so that it yields a pair of 1D problems. Then we propose a numerical scheme which consists of upwind scheme along with a post processing technique. We prove analytically that the proposed algorithm provides almost second-order convergent solution. To corroborate the theoretical result, we provide numerical examples. [ABSTRACT FROM AUTHOR]

Thermal barrier coating (TBC) systems have long been used in many engineering applications, such as jet engines and gas turbines. One pressing task is to evaluate their performance and integrity under long-term thermal cycles. This task requires an accurate and efficient time integration technique that is unconditionally stable, since large time steps are required to simulate TBC systems under long-term thermal effects. In this work, we present in detail several numerical methods to model the thermomechanically coupled responses of TBC systems, including a monolithic approach and two staggered approaches based on the isothermal split and the adiabatic split, respectively. We also demonstrate several finite element simulation techniques, such as the periodic boundary conditions and the adaptive mesh refinement, in the modeling of TBC systems. Through several numerical examples, we show that the staggered approach based on the adiabatic split preserves the unconditional stability of individual time integration techniques used for the mechanical phase and the thermal phase of the coupled problem. Moreover, the computational cost is significantly lower compared to the monolithic approach. This work provides an efficient time integration approach to model more complex behaviors of TBC systems under long-term thermal cycles. • Thermomechanically coupled responses of thermal barrier coating are investigated. • Time integration methods based on monolithic and staggered approaches are presented. • Staggered approach based on adiabatic split preserves unconditional stability. • Periodic boundary conditions and adaptive mesh refinement improve efficiency. • Stress concentration at interfaces inside thermal barrier coating is demonstrated. [ABSTRACT FROM AUTHOR]

This article presents an efficient stabilized finite element scheme for solving viscoelastic flow problems at highWeissenberg numbers. The velocity and pressure variables in the momentum balance equations are uncoupled using an incremental fractional step method based on the second-order backward differentiation formula. The pressure gradient projection stabilization technique and the discrete elastic-viscous-split-stress formulation are introduced into the scheme, in explicit versions, to circumvent the LBB constraints. For the constitutive equation, a square root transformation is first applied to preserve the positive definiteness of the polymer conformation tensor, and then the streamline upwind/Petrov--Galerkin method and the second-order Runge--Kutta scheme are implemented for spatial and time discretizations. Three benchmark problems are tested and numerical results have revealed the accuracy and convergence of the scheme. What is more, since the presented scheme enables the use of equal low-order interpolations for all variables, and requires no iterative process, it is computationally efficient and easy to be implemented. [ABSTRACT FROM AUTHOR]

The dynamics of death of cardiac muscle cells in the acute phase of myocardial infarction is studied numerically. The problem is considered in local and spatially distributed formulations. The adequacy of the mathematical model is confirmed by the quantitative agreement between the results of numerical solution of the problem and experimental data. The adopted models are used to investigate the trigger mechanism of transition from a favorable scenario for the development of acute myocardial infarction to a scenario with a rapid increase in the level of myocardial damage on the third–fifth day of myocardial infarction. For these scenarios of the development of myocardial infarction, the process of demarcating inflammation is investigated. The results of the studies, including evaluations of the effectiveness of anti-inflammatory cytokine therapeutic strategies, are consistent with available data of laboratory studies. [ABSTRACT FROM AUTHOR]

This study concerns the computational accuracy of a particle method for a time-dependent incompressible flow. In recent years, accurate spatial discretization schemes have been developed for a particle method. However, the actual convergence rate in space tends to be much lower than the order of the leading truncation error given by an adopted spatial discretization scheme. This suggests that the Δt-dependent error is comparably significant with respect to the truncation error of the spatial discretization scheme. Under these circumstances, we have developed a new time marching method to improve the computational accuracy by reducing the Δt-dependent error and improving the convergence property. The proposed time marching method is based on the 1st-order fractional step method, just as the conventional methods. However, as opposed to the past studies, the convection term is explicitly included in the provisional velocity calculation, as an Eulerian-based approach. By doing this, the Δt-dependent error caused by the particle movement can be avoided. A numerical test has been carried out using the two-dimensional Taylor-Green vortex problem, where 2nd- and 4th-order spatial discretization schemes are adopted. As a result, the conventional time marching methods gave much lower convergence rate than the order of the spatial discretization scheme. On the other hand, the proposed time marching method showed approximately 2nd- and 4th-order convergence in space with the 2nd- and 4th-order spatial discretization schemes, respectively. Therefore, the proposed method is indicated to highly improve the computational accuracy.

Summary: We propose a new approach for reconstructing velocity boundary conditions in sharp‐inerface immersed boundary (IB) methods based on the moving least squares (MLS) interpolation method. The MLS is employed to not only reconstruct velocity boundary conditions but also to calculate the pressure and velocity gradients in the vicinity of the immersed body, which are required in fluid structure interaction problems to obtain the force exerted by the fluid on the structure. To extend the method to arbitrarily complex geometries with nonconvex shaped boundaries, the visibility method is combined with the MLS method. The performance of the proposed curvilinear IB MLS (CURVIB‐MLS) is demonstrated by systematic grid‐refinement studies for two‐ and three‐dimensional tests and compared with the standard CURVIB method employing standard wall‐normal interpolation for reconstructing boundary conditions. The test problems are flow in a lid‐driven cavity with a sphere, uniform flow over a sphere, flow on a NACA0018 airfoil at incidence, and vortex‐induced vibration of an elastically‐mounted cylinder. We show that the CURVIB‐MLS formulation yields a method that is easier to implement in complex geometries and exhibits higher accuracy and rate of convergence relative to the standard CURVIB method. The MLS approach is also shown to dramatically improve the accuracy of calculating the pressure and viscous forces imparted by the flow on the body and improve the overall accuracy of FSI simulations. Finally, the CURVIB‐MLS approach is able to qualitatively capture on relatively coarse grids important features of complex separated flows that the standard CURVIB method is able to capture only on finer grids. Moving least squares interpolation is proposed for accurate reconstruction of boundary conditions in the vicinity of immersed bodies in the sharp interface immersed boundary method. A visibility method is incorporated into the algorithm to enhance accuracy and accelerate reconstruction at nodes near sharp edges. The performance of the proposed method is evaluated for a series of canonical flow fluid problems. [ABSTRACT FROM AUTHOR]

In option pricing models with correlated stochastic processes, an option premium is commonly a solution to a partial differential equation (PDE) with mixed derivatives in more than two space dimensions. Alternating direction implicit (ADI) finite difference methods are popular for solving a PDE with more than two space dimensions; however, it is not straightforward to employ the ADI method for solving a PDE with mixed derivatives. The aim of this study is to find out which numerical method would be appropriate to solve PDEs with mixed derivatives based on the accuracy of the solutions and the computation time. This study applies the fractional step method and the radial basis functions to solve a PDE with a mixed derivative, and investigates the efficiency of these numerical methods. Numerical experiments are conducted by applying these methods to exchange option pricing; exchange options are selected because the exchange option premium has an analytical form. The numerical results show that the both methods calculate premiums with high accuracy in the presence of mixed derivatives. The fractional step method calculates the option premium more accurately and much faster than the radial basis functions. Therefore, from the numerical experiments, this study concludes that the fractional step method is more appropriate than the radial basis functions for solving a PDE with a mixed derivative.

The Jin-Neelin model for the El Niño-Southern Oscillation (ENSO for short) is considered for which the authors establish existence and uniqueness of global solutions in time over an unbounded channel domain. The result is proved for initial data and forcing that are sufficiently small. The smallness conditions involve in particular key physical parameters of the model such as those that control the travel time of the equatorial waves and the strength of feedback due to vertical-shear currents and upwelling; central mechanisms in ENSO dynamics.From the mathematical view point, the system appears as the coupling of a linear shallow water system and a nonlinear heat equation. Because of the very different nature of the two components of the system, the authors find it convenient to prove the existence of solution by semi-discretization in time and utilization of a fractional step scheme. The main idea consists of handling the coupling between the oceanic and temperature components by dividing the time interval into small sub-intervals of length k and on each sub-interval to solve successively the oceanic component, using the temperature T calculated on the previous sub-interval, to then solve the sea-surface temperature (SST for short) equation on the current sub-interval. The passage to the limit as k tends to zero is ensured via a priori estimates derived under the aforementioned smallness conditions. [ABSTRACT FROM AUTHOR]

Abstract A numerical method to achieve the simultaneous computation of the seepage flows in porous media and the Navier-Stokes flows in the domain occupied purely by a fluid is presented in this paper. The method uses the Darcy-Brinkman equations with the continuous modelling of the interfacial flow velocity, and applies the finite volume method to the spatial discretization and the fractional step method to the numerical simulation of the incompressible fluid. The coupling of the two different flows is realized by the relevant interpolation of the pressure and the flow velocity onto the interface at which permeability and porosity are discontinuous. The interpolation schemes provide simple solutions to overcome the computational instability caused by the discontinuous change in permeability and to avoid having to resolve the considerably thin transition zone near the interface. Numerical analyses of the one-dimensional uniform flow, the lid-driven cavity flow, and the pipe-flow in a porous medium have been carried out. The results have shown that the proposed schemes enable a stable computation and fulfill the accurate and physically realistic numerical solutions. [ABSTRACT FROM AUTHOR]

A simple spatially discrete model problem consisting of mass points and dash-pots is presented which allows for the assessment of the properties of different projection schemes for the solution of the incompressible Navier–Stokes equations. In particular, the temporal accuracy, the stability and the numerical damping are investigated. The present study suggests that it is not possible to formulate a second order accurate projection/pressure-correction scheme which possesses any high-frequency damping. Motivated by this observation two new families of projection schemes are proposed which are developed from the generalised midpoint rule and from the generalised- α method, respectively, and offer control over high-frequency damping. Both schemes are investigated in detail on the basis of the model problem and subsequently implemented in the context of a finite element formulation for the incompressible Navier–Stokes equations. Comprehensive numerical studies of the flow in a lid-driven cavity and the flow around a cylinder are presented. The observations made are in agreement with the conclusions drawn from the model problem. [ABSTRACT FROM AUTHOR]

ABSTRACT Lee, J.L.; Kim, J.W.; Kim, H.S.; Cho, W.C., and Lee, J., 2018. Development of prediction system for invasion of swell-like waves on the southern coast of Korea. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 706–710. Coconut Creek (Florida), ISSN 0749-0208. Recently, several drowning accidents caused by rip currents were reported along Haeundae Beach, located at the southeastern corner of the Korean Peninsula. Several dozen people were swept away by rip currents, and subsequently rescued between August 7 and 10, 2012. The main cause of rip currents is swell waves that approach the shore. The rip current becomes more dangerous when a relatively long-period swell-like wave invades and is intensified, during the passage of typhoons far off shore. However, existing wind wave models require significant computational cost and time to obtain solutions to a set of partial differential equations, and have low accuracy for predicting the invasion of swell-like waves on coasts because they simultaneously calculate wind wave generation and wave propagation. In this study, we used a fractional step method to solve the wind wave generation and swell wave propagation components, in which the former is simulated using a typical spectrum approach and the latter is simulated using a Lagrangian approach. The results from the theoretical model were compared with field data collected during the dangerous rip current events in August 2012. [ABSTRACT FROM AUTHOR]

This study presents an improved semi-implicit MPM formulation for coupled large deformation problems in geotechnics based on the fractional step method. The main objective of this study is to make the choice of the time step size independent of the permeability and to reduce the pressure oscillations by applying the special splitting procedure and the stabilized technique. The proposed coupled MPM is validated by comparing numerical results with analytical solutions of the one-dimensional consolidation problem in both small and large deformation regimes. Three numerical tests are performed to further evaluate the performance of the proposed method, including a self-weight slumping block, 2D consolidation test, and the stability of a saturated elasto-plastic slope. The numerical results indicate that the proposed method is suitable for simulating fluid-saturated porous media involving large deformation. [ABSTRACT FROM AUTHOR]

We consider a time semi-discretization of the Caginalp phase-field model based on an operator splitting method. For every time-step parameter τ, we build an exponential attractor Mτ of the discrete-in-time dynamical system. We prove that Mτ converges to an exponential attractor M0 of the continuous-in-time dynamical system for the symmetric Hausdorff distance as τ tends to 0. We also provide an explicit estimate of this distance and we prove that the fractal dimension of Mτ is bounded by a constant independent of τ. [ABSTRACT FROM AUTHOR]

A novel implicit immersed boundary method of high accuracy and efficiency is presented for the simulation of incompressible viscous flow over complex stationary or moving solid boundaries. A boundary force is often introduced in many immersed boundary methods to mimic the presence of solid boundary, such that the overall simulation can be performed on a simple Cartesian grid. The current method inherits this idea and considers the boundary force as a Lagrange multiplier to enforce the no-slip constraint at the solid boundary, instead of applying constitutional relations for rigid bodies. Hence excessive constraint on the time step is circumvented, and the time step only depends on the discretization of fluid Navier-Stokes equations, like the CFL condition in present work. To determine the boundary force, an additional moving force equation is derived. The dimension of this derived system is proportional to the number of Lagrangian points describing the solid boundaries, which makes the method very suitable for moving boundary problems since the time for matrix update and system solving is not significant. The force coefficient matrix is made symmetric and positive definite so that the conjugate gradient method can solve the system quickly. The proposed immersed boundary method is incorporated into the fluid solver with a second-order accurate projection method as a plug-in. The overall scheme is handled under an efficient fractional step framework, namely, prediction, forcing, and projection. Various simulations are performed to validate current method, and the results compare well with previous experimental and numerical studies. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study in which several partitioned solution procedures for incompressible fluid-structure interaction are compared and validated against the results of an experimental fluid-structure interaction benchmark. The numerical methods discussed cover the three main families of coupling schemes: strongly coupled, semi-implicit, and loosely coupled. Very good agreement is observed between the numerical and experimental results. The comparisons confirm that strong coupling can be efficiently avoided, via semi-implicit and loosely coupled schemes, without compromising stability and accuracy. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The main goal of this paper is the numerical solution of the Navier-Stokes equations for an incompressible flow. A numerical approach with a finite volume discretization technique and using the method of fractional stepsare presented to solver the coupling between velocity and pressure. In order to validate the mathematical model and the code a the Driven Cavity problem in two dimensions for Reynolds numbers between 100 and 1000 was solved. The results given by the code are very similar to the expected. In order to verify the numerical results a h-refinement study is carried out.

In This study develops a quasi-three dimensional numerical model of wave driven coastal currents with accounting the effects of the wave-current interaction and the surface rollers. In the wave model, the current effects on wave breaking and energy dissipation are taken into account as well as the wave diffraction effect. The surface roller associated with wave breaking was modeled based on a modification of the equations by Dally and Brown (1995) and Larson and Kraus (2002). Furthermore, the quasi-three dimensional model, which based on Navier-Stokes equations, was modified in association with the surface roller effect, and solved using frictional step method. The model was validated by data sets obtained during experiments on the Large Scale Sediment Transport Facility (LSTF) basin and the Hazaki Oceanographical Research Station (HORS). Then, a model test against detached breakwater was carried out to investigate the performance of the model around coastal structures. Finally, the model was applied to Akasaki port to verify the hydrodynamics around coastal structures. Good agreements between computations and measurements were obtained with regard to the cross-shore variation in waves and currents in nearshore and surf zone.

A numerical model was developed for simulating a three-dimensional multilayer hydrodynamic and thermodynamic model in domains with irregular bottom topography. The model was designed for examining the interactions between flow and topography. The model was based on the three-dimensional Navier-Stokes equations and was solved using the fractional step method, which combines the finite difference method in the horizontal plane and the finite element method in the vertical plane. The numerical techniques were described and the model test and application were presented. For the model application to the northern part of Ariake Sea, the hydrodynamic and thermodynamic results were predicted. The numerically predicted amplitudes and phase angles were well consistent with the field observations.

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