共查询到20条相似文献,搜索用时 62 毫秒
1.
2.
We derive a tensor artificial viscosity suitable for use in a 2D or 3D unstructured arbitrary Lagrangian–Eulerian (ALE) hydrodynamics code. This work is similar in nature to that of Campbell and Shashkov [1]; however, our approach is based on a finite element discretization that is fundamentally different from the mimetic finite difference framework. The finite element point of view leads to novel insights as well as improved numerical results. We begin with a generalized tensor version of the Von Neumann–Richtmyer artificial viscosity, then convert it to a variational formulation and apply a Galerkin discretization process using high order Gaussian quadrature to obtain a generalized nodal force term and corresponding zonal heating (or shock entropy) term. This technique is modular and is therefore suitable for coupling to a traditional staggered grid discretization of the momentum and energy conservation laws; however, we motivate the use of such finite element approaches for discretizing each term in the Euler equations. We review the key properties that any artificial viscosity must possess and use these to formulate specific constraints on the total artificial viscosity force term as well as the artificial viscosity coefficient. We also show, that under certain simplifying assumptions, the two-dimensional scheme from [1] can be viewed as an under-integrated version of our finite element method. This equivalence holds on general distorted quadrilateral grids. Finally, we present computational results on some standard shock hydro test problems, as well as some more challenging problems, indicating the advantages of the new approach with respect to symmetry preservation for shock wave propagation over general grids. 相似文献
3.
A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier–Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied. 相似文献
4.
G. Carré S. Del PinoB. Després E. Labourasse 《Journal of computational physics》2009,228(14):5160-5183
We describe a cell-centered Godunov scheme for Lagrangian gas dynamics on general unstructured meshes in arbitrary dimension. The construction of the scheme is based upon the definition of some geometric vectors which are defined on a moving mesh. The finite volume solver is node based and compatible with the mesh displacement. We also discuss boundary conditions. Numerical results on basic 3D tests problems show the efficiency of this approach. We also consider a quasi-incompressible test problem for which our nodal solver gives very good results if compared with other Godunov solvers. We briefly discuss the compatibility with ALE and/or AMR techniques at the end of this work. We detail the coefficients of the isoparametric element in the appendix. 相似文献
5.
Based on the integral form of the fluid dynamic equations, a finite volume kinetic scheme with arbitrary control volume and mesh velocity is developed. Different from the earlier unified moving mesh gas-kinetic method [C.Q. Jin, K. Xu, An unified moving grid gas-kinetic method in Eulerian space for viscous flow computation, J. Comput. Phys. 222 (2007) 155–175], the coupling of the fluid equations and geometrical conservation laws has been removed in order to make the scheme applicable for any quadrilateral or unstructured mesh rather than parallelogram in 2D case. Since a purely Lagrangian method is always associated with mesh entangling, in order to avoid computational collapsing in multidimensional flow simulation, the mesh velocity is constructed by considering both fluid velocity (Lagrangian methodology) and diffusive velocity (Regenerating Eulerian mesh function). Therefore, we obtain a generalized Arbitrary-Lagrangian–Eulerian (ALE) method by properly designing a mesh velocity instead of re-generating a new mesh after distortion. As a result, the remapping step to interpolate flow variables from old mesh to new mesh is avoided. The current method provides a general framework, which can be considered as a remapping-free ALE-type method. Since there is great freedom in choosing mesh velocity, in order to improve the accuracy and robustness of the method, the adaptive moving mesh method [H.Z. Tang, T. Tang, Adaptive mesh methods for one-and two-dimensional hyperbolic conservation laws, SIAM J. Numer. Anal. 41 (2003) 487–515] can be also used to construct a mesh velocity to concentrate mesh to regions with high flow gradients. 相似文献
6.
This work presents a multi-dimensional cell-centered unstructured finite volume scheme for the solution of multimaterial compressible fluid flows written in the Lagrangian formalism. This formulation is considered in the Arbitrary-Lagrangian–Eulerian (ALE) framework with the constraint that the mesh velocity and the fluid velocity coincide. The link between the vertex velocity and the fluid motion is obtained by a formulation of the momentum conservation on a class of multi-scale encased volumes around mesh vertices. The vertex velocity is derived with a nodal Riemann solver constructed in such a way that the mesh motion and the face fluxes are compatible. Finally, the resulting scheme conserves both momentum and total energy and, it satisfies a semi-discrete entropy inequality. The numerical results obtained for some classical 2D and 3D hydrodynamic test cases show the robustness and the accuracy of the proposed algorithm. 相似文献
7.
8.
We present a new cell-centered Lagrangian scheme on unstructured mesh for hyperelasticity. It is based on the recently proposed Glace scheme [11] for compressible gas dynamics. We show how to use the multiplicative decomposition of the gradient of deformation and the entropy property to derive the new scheme. We also prove the compatibility of this discretization with usual calculations of mass. Our motivation is to use hyperelasticity models for the study of finite plasticity, which is an extension of hypoelasticity to finite deformations. Hyperelasticity is a natural choice for extended models in solid mechanics, because of its mathematical structure which is a system of conservation laws with full rotational invariance. We study these properties for the Lagrangian system, and detail the various Eulerian formulations. 相似文献
9.
10.
11.
Yu Wang Songhe Song Zhijun Tan Desheng Wang 《Journal of computational physics》2009,228(17):6333-6348
This paper presents an adaptive method for variational curve smoothing based on level set implementation. A suitable cost functional is minimized via solving the derived Euler–Lagrangian equation, of which the discretization is conducted on unstructured triangular meshes by employing a simple and effective finite volume scheme. Through adaptive refinement of the mesh, the geometry features of the given curve can be well resolved in a cost-effective way. Various numerical experiments demonstrate the effectiveness and efficiency of the proposed approach. 相似文献
12.
Luciano Gonç alves Noleto Manuel N. D. Barcelos Jr. & Antonio C. P. Brasil Jr. 《advances in applied mathematics and mechanics.》2013,5(2):194-211
This work presents a moving mesh methodology based on the solution
of a pseudo flow problem. The mesh motion is modeled as a pseudo Stokes
problem solved by an explicit finite element projection method. The mesh
quality requirements are satisfied by employing a null divergent velocity
condition. This methodology is applied to triangular unstructured meshes
and compared to well known approaches such as the ones based on diffusion
and pseudo structural problems. One of the test cases is an airfoil with
a fully meshed domain. A specific rotation velocity is imposed as the
airfoil boundary condition. The other test is a set of two cylinders
that move toward each other. A mesh quality criterion is employed to
identify critically distorted elements and to evaluate the performance
of each mesh motion approach. The results obtained for each test case
show that the pseudo-flow methodology produces satisfactory meshes
during the moving process. 相似文献
13.
A new reconstruction algorithm is proposed for constructing cell-centered diffusion schemes on distorted meshes. Its main feature is that edge unknowns are defined at certain balance points, the locations of which depend on the diffusion coefficient and the skewness of grid cells, so as to obtain a two-point reconstruction stencil. Implementing the new algorithm for the approximation of gradients, we extend the IDC (improved deferred correction) scheme, which was proposed by Traoré et al. [P. Traoré, Y. Ahipo, C. Louste, A robust and efficient finite volume scheme for the discretization of diffusive flux on extremely skewed meshes in complex geometries, J. Comput. Phys. 228 (2009) 5148–5159], to handle diffusion problems with discontinuous coefficients. Numerical results demonstrate the accuracy and efficiency of the extended scheme. 相似文献
14.
In this paper, an unstructured cell-centered second-order accurate finite volume method is presented for the computation of electrical conditions inside wire-plate electrostatic precipitators. The potential equation was discretized using a second-order accurate scheme by invoking a new type of special line-structure. The space–charge density equation was discretized using a second-order upwind scheme, and solved using a new direct method. The local gradients are reconstructed by a weighted least-square reconstruction method. The method can deal with complex geometries by using unstructured meshes. Numerical experiments show that the predicted results agree well with the existing experimental data. 相似文献
15.
The consistent and conservative scheme developed on a rectangular collocated mesh [M.-J. Ni, R. Munipalli, N.B. Morley, P. Huang, M.A. Abdou, A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part I: on a rectangular collocated grid system, Journal of Computational Physics 227 (2007) 174–204] and on an arbitrary collocated mesh [M.-J. Ni, R. Munipalli, P. Huang, N.B. Morley, M.A. Abdou, A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part II: on an arbitrary collocated mesh, Journal of Computational Physics 227 (2007) 205–228] has been extended and specially designed for calculation of the Lorentz force on a staggered grid system (Part III) by solving the electrical potential equation for magnetohydrodynamics (MHD) at a low magnetic Reynolds number. In a staggered mesh, pressure (p) and electrical potential (φ) are located in the cell center, while velocities and current fluxes are located on the cell faces of a main control volume. The scheme numerically meets the physical conservation laws, charge conservation law and momentum conservation law. Physically, the Lorentz force conserves the momentum when the magnetic field is constant or spatial coordinate independent. The calculation of current density fluxes on cell faces is conducted using a scheme consistent with the discretization for solution of the electrical potential Poisson equation, which can ensure the calculated current density conserves the charge. A divergence formula of the Lorentz force is used to calculate the Lorentz force at the cell center of a main control volume, which can numerically conserve the momentum at constant or spatial coordinate independent magnetic field. The calculated cell-center Lorentz forces are then interpolated to the cell faces, which are used to obtain the corresponding velocity fluxes by solving the momentum equations. The “conservative” is an important property of the scheme, which can guarantee computational accuracy of MHD flows at high Hartmann number with a strongly non-uniform mesh employed to resolve the Hartmann layers and side layers. 2D fully developed MHD flows with analytical solutions available have been conducted to validate the scheme at a staggered mesh. 3D MHD flows, with the experimental data available, at a constant magnetic field in a rectangular duct with sudden expansion and at a varying magnetic field in a rectangular duct are conducted on a staggered mesh to verify the computational accuracy of the scheme. It is expected that the scheme for the Lorentz force can be employed together with a fully conservative scheme for the convective term and the pressure term [Y. Morinishi, T.S. Lund, O.V. Vasilyev, P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, Journal of Computational Physics 143 (1998) 90–124] for direct simulation of MHD turbulence and MHD instability with good accuracy at a staggered mesh. 相似文献
16.
We are interested in a robust and accurate finite volume scheme for 2-D parabolic problems derived from the cell functional minimization approach. The scheme has a local stencil, is locally conservative, treats discontinuity rigorously and leads to a symmetric positive definite linear system. Since the scheme has both cell centered unknowns and cell edge unknowns, the computational cost is an issue and a parallel algorithm is then suggested based on nonoverlapping domain decomposition approach. The interface condition is of the Dirichlet–Robin type and has a parameter λ. By choosing this parameter properly, the convergence of the iteration process could be sped up. Numerical results for linear and nonlinear problems demonstrate the good performance of the cell functional minimization scheme and its parallel version on distorted meshes. 相似文献
17.
18.
19.
提出一种液舱横荡数值模拟的方法,将气液两相交界面视为物理间断,通过高阶精度离散格式捕捉间断.根据NVD(Normalized Variable Diagram)实现非结构化网格上高精度离散格式,建立固定网格上自由表面运动模拟方法.在开发的非结构网格有限体积法求解器GTEA(General Transport Equation Analyzer)基础上,实现上述方法.首先对经典的溃坝过程进行模拟,并与文献结果对比验证方法和程序的可信度.对二维矩形液舱在不同激振频率时的横荡进行数值计算,并与实验以及商业软件CFX计算结果进行比较.结果表明方法和软件可以模拟自由面的翻卷、破碎运动现象,对距自由面较深点处流体载荷的计算结果与实验值符合较好,与商业软件CFX相比,在相同计算网格下,算法可以更好的计算次峰值,验证方法正确可行. 相似文献
20.
Caterina Calgaro Emile Chane-Kane Emmanuel Creusé Thierry Goudon 《Journal of computational physics》2010,229(17):6027-6046
This work is devoted to the design of multi-dimensional finite volume schemes for solving transport equations on unstructured grids. In the framework of MUSCL vertex-based methods we construct numerical fluxes such that the local maximum property is guaranteed under an explicit Courant–Friedrichs–Levy condition. The method can be naturally completed by adaptive local mesh refinements and it turns out that the mesh generation is less constrained than when using the competitive cell-centered methods. We illustrate the effectiveness of the scheme by simulating variable density incompressible viscous flows. Numerical simulations underline the theoretical predictions and succeed in the computation of high density ratio phenomena such as a water bubble falling in air. 相似文献