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Parallel computing has become an important subject in the field of computer science and has proven to be critical when researching high performance solutions. The evolution of computer architectures (multi-core and many-core) towards a higher number of cores can only confirm that parallelism is the method of choice for speeding up an algorithm. In the last decade, the graphics processing unit, or GPU, has gained an important place in the field of high performance computing (HPC) because of its low cost and massive parallel processing power. Super-computing has become, for the first time, available to anyone at the price of a desktop computer. In this paper, we survey the concept of parallel computing and especially GPU computing. Achieving efficient parallel algorithms for the GPU is not a trivial task, there are several technical restrictions that must be satisfied in order to achieve the expected performance. Some of these limitations are consequences of the underlying architecture of the GPU and the theoretical models behind it. Our goal is to present a set of theoretical and technical concepts that are often required to understand the GPU and its massive parallelism model. In particular, we show how this new technology can help the field of computational physics, especially when the problem is data-parallel. We present four examples of computational physics problems; n-body, collision detection, Potts model and cellular automata simulations. These examples well represent the kind of problems that are suitable for GPU computing. By understanding the GPU architecture and its massive parallelism programming model, one can overcome many of the technical limitations found along the way, design better GPU-based algorithms for computational physics problems and achieve speedups that can reach up to two orders of magnitude when compared to sequential implementations.
In this paper we present recent developments concerning a Cell-Centered Arbitrary Lagrangian Eulerian (CCALE) strategy using the Moment Of Fluid (MOF) interface reconstruction for the numerical simulation of multi-material compressible fluid flows on unstructured grids in cylindrical geometries. Especially, our attention is focused here on the following points. First, we propose a new formulation of the scheme used during the Lagrangian phase in the particular case of axisymmetric geometries. Then, the MOF method is considered for multi-interface reconstruction in cylindrical geometry. Subsequently, a method devoted to the rezoning of polar meshes is detailed. Finally, a generalization of the hybrid remapping to cylindrical geometries is presented. These explorations are validated by mean of several test cases using unstructured grid that clearly illustrate the robustness and accuracy of the new method.
The evolution of precipitates in stressed solids is modeled by coupling a quasi-steady diffusion equation and a linear elasticity equation with dynamic boundary conditions. The governing equations are solved numerically using a boundary integral method (BIM). A critical step in applying BIM is to develop fast algorithms to reduce the arithmetic operation count of matrix-vector multiplications. In this paper, we develop a fast adaptive treecode algorithm for the diffusion and elasticity problems in two dimensions (2D). We present a novel source dividing strategy to parallelize the treecode. Numerical results show that the speedup factor is nearly perfect up to a moderate number of processors. This approach of parallelization can be readily implemented in other treecodes using either uniform or non-uniform point distribution. We demonstrate the effectiveness of the treecode by computing the long-time evolution of a complicated microstructure in elastic media, which would be extremely difficult with a direct summation method due to CPU time constraint. The treecode speeds up computations dramatically while fulfilling the stringent precision requirement dictated by the spectrally accurate BIM.
Compressible flow past a circular cylinder at an inflow Reynolds number of 2 x 105 is numerically investigated by using a constrained large-eddy simulation (CLES) technique. Numerical simulation with adiabatic wall boundary condition and at a free-stream Mach number of 0.75 is conducted to validate and verify the performance of the present CLES method in predicting separated flows. Some typical and characteristic physical quantities, such as the drag coefficient, the root-mean-square lift fluctuations, the Strouhal number, the pressure and skin friction distributions around the cylinder, etc. are calculated and compared with previously reported experimental data, finer-grid large-eddy simulation (LES) data and those obtained in the present LES and detached-eddy simulation (DES) on coarse grids. It turns out that CLES is superior to DES in predicting such separated flow and that CLES can mimic the intricate shock wave dynamics quite well. Then, the effects of Mach number on the flow patterns and parameters such as the pressure, skin friction and drag coefficients, and the cylinder surface temperature are studied, with Mach number varying from 0.1 to 0.95. Non-monotonic behaviors of the pressure and skin friction distributions are observed with increasing Mach number and the minimum mean separation angle occurs at a subcritical Mach number of between 0.3 and 0.5. Additionally, the wall temperature effects on the thermodynamic and aerodynamic quantities are explored in a series of simulations using isothermal wall boundary conditions at three different wall temperatures. It is found that the flow separates earlier from the cylinder surface with a longer recirculation length in the wake and a higher pressure coefficient at the rear stagnation point for higher wall temperature. Moreover, the influences of different thermal wall boundary conditions on the flow field are gradually magnified from the front stagnation point to the rear stagnation point. Moreover, the influences of different thermal wall boundary conditions on the flow field are graduallymagnified from the front stagnation point to the rear stagnation point. It is inferred that the CLES approach in its current version is a useful and effective tool for simulating wall-bounded compressible turbulent flows with massive separations.
In plasma physics domain, the electron transport is described with the Fokker-Planck-Landau equation. The direct numerical solution of the kinetic equation is usually intractable due to the large number of independent variables. That is why we propose in this paper a new model whose derivation is based on an angular closure in the phase space and retains only the energy of particles as kinetic dimension. To find a solution compatible with physics conditions, the closure of the moment system is obtained under a minimum entropy principle. This model is proved to satisfy the fundamental properties like a H theorem. Moreover an entropic discretization in the velocity variable is proposed on the semi-discrete model. Finally, we validate on numerical test cases the fundamental properties of the full discrete model.
In this paper, a numerical method is presented for simulating the 3D interfacial flows with insoluble surfactant. The numerical scheme consists of a 3D immersed interface method (IIM) for solving Stokes equations with jumps across the interface and a 3D level-set method for solving the surfactant convection-diffusion equation along a moving and deforming interface. The 3D IIM Poisson solver modifies the one in the literature by assuming that the jump conditions of the solution and the flux are implicitly given at the grid points in a small neighborhood of the interface. This assumption is convenient in conjunction with the level-set techniques. It allows standard Lagrangian interpolation for quantities at the projection points on the interface. The interface jump relations are re-derived accordingly. A novel rotational procedure is given to generate smooth local coordinate systems and make effective interpolation. Numerical examples demonstrate that the IIM Poisson solver and the Stokes solver achieve second-order accuracy. A 3D drop with insoluble surfactant under shear flow is investigated numerically by studying the influences of different physical parameters on the drop deformation.
We introduce a new multigrid method to study the lattice statics model arising from nanoindentation. A constrained Cauchy-Born elasticity model is used as the coarse-grid operator. This method accelerates the relaxation process and considerably reduces the computational cost. In particular, it saves quite a bit when dislocations nucleate and move, as demonstrated by the simulation results.
In this paper, we study a lattice Boltzmann method for the advection-diffusion equation with Neumann boundary conditions on general boundaries. A novel mass conservative scheme is introduced for implementing such boundary conditions, and is analyzed both theoretically and numerically.
Second order convergence is predicted by the theoretical analysis, and numerical investigations show that the convergence is at or close to the predicted rate. The numerical investigations include time-dependent problems and a steady-state diffusion problem for computation of effective diffusion coefficients.
We critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification. Here we focus on Stefan problems, and their quasi-static variants, with applications to crystal growth. New approaches with a high mesh quality for the parametric approximations of the resulting free boundary problems and new stable discretizations of the anisotropic phase field system are taken into account in a comparison involving benchmark problems based on exact solutions of the free boundary problem.
The modified embedded atom method (MEAM) with the universal form of embedding function and a modified energy term along with the pair potential has been employed to determine the potentials for alkali metals: Na, K, by fitting to the Cauchy pressure (C12 − C44)/2, shear constants Gν = (C11 − C12 + 3C44)/5 and C44, the cohesive energy and the vacancy formation energy. The obtained potentials are used to calculate the phonon dispersions of these metals. Using these calculated phonons we evaluate the local density of states of neighbours of vacancy using Green’s function method. The local density of states of neighbours of vacancy has been used to calculate mean square displacements of these atoms and formation entropy of vacancy. The calculated mean square displacements of both 1st and 2nd neighbours of vacancy are found to be lower than that of host atom. The calculated phonon dispersions agree well with the experimental phonon dispersion curves and the calculated results of vacancy formation entropy compare well with the other available results.