共查询到10条相似文献，搜索用时 46 毫秒
1.
An approximate‐state Riemann solver for the solution of hyperbolic systems of conservation laws with source terms is proposed. The formulation is developed under the assumption that the solution is made of rarefaction waves. The solution is determined using the Riemann invariants expressed as functions of the components of the flux vector. This allows the flux vector to be computed directly at the interfaces between the computational cells. The contribution of the source term is taken into account in the governing equations for the Riemann invariants. An application to the water hammer equations and the shallow water equations shows that an appropriate expression of the pressure force at the interface allows the balance with the source terms to be preserved, thus ensuring consistency with the equations to be solved as well as a correct computation of steady‐state flow configurations. Owing to the particular structure of the variable and flux vectors, the expressions of the fluxes are shown to coincide partly with those given by the HLL/HLLC solver. Computational examples show that the approximate‐state solver yields more accurate solutions than the HLL solver in the presence of discontinuous solutions and arbitrary geometries. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
2.
Qiuhua Liang 《国际流体数值方法杂志》2012,69(2):442-458
This paper presents a new simplified grid system that provides local refinement and dynamic adaptation for solving the 2D shallow water equations (SWEs). Local refinement is realized by simply specifying different subdivision levels to the cells on a background uniform coarse grid that covers the computational domain. On such a non‐uniform grid, the structured property of a regular Cartesian mesh is maintained and neighbor information is determined by simple algebraic relationships, i.e. data structure becomes unnecessary. Dynamic grid adaptation is achieved by changing the subdivision level of a background cell. Therefore, grid generation and adaptation is greatly simplified and straightforward to implement. The new adaptive grid‐based SWE solver is tested by applying it to simulate three idealized test cases and promising results are obtained. The new grid system offers a simplified alternative to the existing approaches for providing adaptive mesh refinement in computational fluid dynamics. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
3.
This paper aims to reassess the Riemann solver for compressible fluid flows in Lagrangian frame from the viewpoint of modified equation approach and provides a theoretical insight into dissipation mechanism. It is observed that numerical dissipation vanishes uniformly for the Godunov‐type schemes in the sense that associated dissipation matrix has zero determinant if an exact or approximate Riemann solver is used to construct numerical fluxes in the Lagrangian frame. This fact connects to some numerical defects such as the wall‐heating phenomenon and start‐up errors. To cure these numerical defects, a traditional numerical viscosity is added, as well as the artificial heat conduction is introduced via a simple passage of the Lax–Friedrichs type discretization of internal energy. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
4.
In this paper, we present a general Riemann solver which is applied successfully to compute the Euler equations in fluid dynamics with many complex equations of state (EOS). The solver is based on a splitting method introduced by the authors. We add a linear advection term to the Euler equations in the first step, to make the numerical flux between cells easy to compute. The added linear advection term is thrown off in the second step. It does not need an iterative technique and characteristic wave decomposition for computation. This new solver is designed to permit the construction of high‐order approximations to obtain high‐order Godunov‐type schemes. A number of numerical results show its robustness. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
5.
Flooding due to the failure of a dam or dyke has potentially disastrous consequences. This paper presents a Godunov‐type finite volume solver of the shallow water equations based on dynamically adaptive quadtree grids. The Harten, Lax and van Leer approximate Riemann solver with the Contact wave restored (HLLC) scheme is used to evaluate interface fluxes in both wet‐ and dry‐bed applications. The numerical model is validated against results from alternative numerical models for idealized circular and rectangular dam breaks. Close agreement is achieved with experimental measurements from the CADAM dam break test and data from a laboratory dyke break undertaken at Delft University of Technology. Copyright © 2004 John Wiley Sons, Ltd. 相似文献
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7.
Vincent Guinot 《国际流体数值方法杂志》2001,37(3):341-359
Godunov‐type algorithms are very attractive for the numerical solution of discontinuous flows. The reconstruction of the profile inside the cells is crucial to scheme performance. The non‐linear generalization of the discontinuous profile method (DPM) presented here for the modelling of two‐phase flow in pipes uses a discontinuous reconstruction in order to capture shocks more efficiently than schemes using continuous functions. The reconstructed profile is used to define the Riemann problem at cell interfaces by averaging of the components of the variable in the base of eigenvectors over their domain of dependence. Intercell fluxes are computed by solving the Riemann problem with an approximate‐state solver. The adapted treatment of boundary conditions is essential to ensure the quality of the computational results and a specific procedure using virtual cells at both extremities of the computational domain is required. Internal boundary conditions can be treated in the same way as external ones. Application of the DPM to test cases is shown to improve the quality of computational results significantly. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
8.
Long Jiang Alistair G.L. Borthwick Tamás Krámer János Józsa 《International Journal of Computational Fluid Dynamics》2013,27(4):223-237
A horizontally variable density flow model is used to simulate hydraulic bore interactions with idealised urban obstacles. The 2D non-linear shallow water equations are solved using a second-order Monotonic Upstream-centered Schemes for Conservation Laws-Hancock Godunov-type HLLC approximate Riemann scheme. Validation test results are reported for wave propagation over a hump, a constant-density circular dam break and two 1D dam breaks involving different spatial distributions of solute concentration. Detailed parameter studies are then considered for hydraulic bore interactions with single and multiple-square obstacles under subcritical, critical and supercritical flow conditions. In all cases, reflected and diffracted wave patterns are generated immediately after the bore impacts the obstacle(s). Later, the incident bore reconstitutes itself downstream of the obstacle(s). Variable density flows are also considered, with the upstream volumetric concentrations set to values corresponding to water–sediment mixture densities of 1165 and 1495 kg/m3. It is found that the upstream Froude number, gap spacing between obstacles and upstream to downstream density difference influence the strength of the bore–structure interaction, run-up at the front face of the obstacle(s), and subsequent wave–wave interactions. 相似文献
9.
This paper presents an efficient method to simulate the reactive flow for general equation of states with the compressible fluid model coupled with reactive rate equation. The important aspect is to deal with mixture of different phases in one cell, which will inevitably happen in the Eulerian method for reactive flow. Physical variables such as the pressure,velocity, and speed of sound in each cell need to be reconstructed for the Harten‐Lax‐Leer‐Contact (HLLC) Riemann solver, which will result in nonlinear algebra equations, and these reconstructed variables are used to obtain the flux. Numerical examples of stable and unstable detonations with different equation of states demonstrate the accuracy and efficiency of this method. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
10.
This paper studies the Riemann problem for a system of nonlinear degenerate wave equations in elasticity. Since the stress function is neither convex nor concave, the shock condition is degenerate. By introducing a degenerate shock under the generalized shock condition, the global solutions are constructively obtained case by case. 相似文献