共查询到10条相似文献，搜索用时 46 毫秒
1.
The Riemann solver is the fundamental building block in the Godunov‐type formulation of many nonlinear fluid‐flow problems involving discontinuities. While existing solvers are obtained either iteratively or through approximations of the Riemann problem, this paper reports an explicit analytical solution to the exact Riemann problem. The present approach uses the homotopy analysis method to solve the nonlinear algebraic equations resulting from the Riemann problem. A deformation equation defines a continuous variation from an initial approximation to the exact solution through an embedding parameter. A Taylor series expansion of the exact solution about the embedding parameter provides a series solution in recursive form with the initial approximation as the zeroth‐order term. For the nonlinear shallow‐water equations, a sensitivity analysis shows fast convergence of the series solution and the first three terms provide highly accurate results. The proposed Riemann solver is implemented in an existing finite‐volume model with a Godunov‐type scheme. The model correctly describes the formation of shocks and rarefaction fans for both one and two‐dimensional dam‐break problems, thereby verifying the proposed Riemann solver for general implementation. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
2.
A. ARABSHAHI D. L. WHITFIELD 《International Journal of Computational Fluid Dynamics》2013,27(3-4):307-321
SUMMARY An implicit, upwind numerical scheme is presented for computing the unsteady transonic flowfield around complex aircraft configurations. This scheme solves the time-dependent Euler equations with a finite volume method that incorporates a high resolution Riemann solver to define the interface fluxes. A multiblock domain decomposition appproach is used to partition the computational domain into a completely arbitrary arrangement of blocks. However, this work is restricted to C1-continuous grid lines across block boundaries. Consequently, block-block interfaces are treated such as to mimic interior block communication, thus introducing no additional spatial differencing error. Computational results have been obtained for a complete wing-pylon-store configuration with the store in the captive and vertical launch positions. The numerical results for both stationary and dynamic grids have shown favorable agreement with experimental data. 相似文献
3.
A fourth‐order accurate solution method for the three‐dimensional Helmholtz equations is described that is based on a compact finite‐difference stencil for the Laplace operator. Similar discretization methods for the Poisson equation have been presented by various researchers for Dirichlet boundary conditions. Here, the complicated issue of imposing Neumann boundary conditions is described in detail. The method is then applied to model Helmholtz problems to verify the accuracy of the discretization method. The implementation of the solution method is also described. The Helmholtz solver is used as the basis for a fourth‐order accurate solver for the incompressible Navier–Stokes equations. Numerical results obtained with this Navier–Stokes solver for the temporal evolution of a three‐dimensional instability in a counter‐rotating vortex pair are discussed. The time‐accurate Navier–Stokes simulations show the resolving properties of the developed discretization method and the correct prediction of the initial growth rate of the three‐dimensional instability in the vortex pair. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
4.
A new mesh‐patching model is presented for shallow water flow described by the 2D non‐linear shallow water (NLSW) equations. The mesh‐patching model is based on AMAZON, a high‐resolution NLSW engine with an improved HLLC approximate Riemann solver. A new patching algorithm has been developed, which not only provides improved spatial resolution of flow features in particular parts of the mesh, but also simplifies and speeds up the (structured) grid generation process for an area with complicated geometry. The new patching technique is also compatible with increasingly popular parallel computing and adaptive grid techniques. The patching algorithm has been tested with moving bores, and results of test problems are presented and compared to previous work. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
5.
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
6.
A complementary set of Reynolds‐averaged Navier–Stokes (RANS) equations has been developed for steady incompressible, turbulent flows. The method is based on the Helmholtz decomposition of the velocity vector field into a viscous and a potential components. In the complementary RANS solver a potential solution coexists with a viscous solution with the purpose of contributing to a fastest decay of the viscous solution in the far field. The proposed complementary RANS equations have been validated for steady laminar and turbulent flows. The computational results show that the complementary RANS solver is able to produce less grid‐dependent solutions than a conventional RANS solver. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
7.
E. F. Toro 《国际流体数值方法杂志》2006,52(4):433-453
The scope of this paper is three fold. We first formulate upwind and symmetric schemes for hyperbolic equations with non‐conservative terms. Then we propose upwind numerical schemes for conservative and non‐conservative systems, based on a Riemann solver, the initial conditions of which are evolved non‐linearly in time, prior to a simple linearization that leads to closed‐form solutions. The Riemann solver is easily applied to complicated hyperbolic systems. Finally, as an example, we formulate conservative schemes for the three‐dimensional Euler equations for general compressible materials and give numerical results for a variety of test problems for ideal gases in one and two space dimensions. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
8.
An upstream flux‐splitting finite‐volume (UFF) scheme is proposed for the solutions of the 2D shallow water equations. In the framework of the finite‐volume method, the artificially upstream flux vector splitting method is employed to establish the numerical flux function for the local Riemann problem. Based on this algorithm, an UFF scheme without Jacobian matrix operation is developed. The proposed scheme satisfying entropy condition is extended to be second‐order‐accurate using the MUSCL approach. The proposed UFF scheme and its second‐order extension are verified through the simulations of four shallow water problems, including the 1D idealized dam breaking, the oblique hydraulic jump, the circular dam breaking, and the dam‐break experiment with 45° bend channel. Meanwhile, the numerical performance of the UFF scheme is compared with those of three well‐known upwind schemes, namely the Osher, Roe, and HLL schemes. It is demonstrated that the proposed scheme performs remarkably well for shallow water flows. The simulated results also show that the UFF scheme has superior overall numerical performances among the schemes tested. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
9.
In this work we analyze the reactive Riemann problem for thermally perfect gases in the deflagration or detonation regimes. We restrict our attention to the case of one irreversible infinitely fast chemical reaction; we also suppose that, in the initial condition, one state (for instance the left one) is burnt and the other one is unburnt. The indeterminacy of the deflagration regime is removed by imposing a (constant) value for the fundamental flame speed of the reactive shock. An iterative algorithm is proposed for the solution of the reactive Riemann problem. Then the reactive Riemann problem and the proposed algorithm are investigated from a numerical point of view in the case in which the unburnt state consists of a stoichiometric mixture of hydrogen and air at almost atmospheric condition. In particular, we revisit the problem of 1D plane‐symmetric steady flames in a semi‐infinite domain and we verify that the transition from one combustion regime to another occurs continuously with respect to the fundamental flame speed and the so‐called piston velocity. Finally, we use the ‘all shock’ solution of the reactive Riemann problem to design an approximate (‘all shock’) Riemann solver. 1D and 2D flows at different combustion regimes are computed, which shows that the approximate Riemann solver, and thus the algorithm we use for the solution of the reactive Riemann problem, is robust in both the deflagration and detonation regimes. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
10.
An algorithm, based on the overlapping control volume (OCV) method, for the solution of the steady and unsteady two‐dimensional incompressible Navier–Stokes equations in complex geometry is presented. The primitive variable formulation is solved on a non‐staggered grid arrangement. The problem of pressure–velocity decoupling is circumvented by using momentum interpolation. The accuracy and effectiveness of the method is established by solving five steady state and one unsteady test problems. The numerical solutions obtained using the technique are in good agreement with the analytical and benchmark solutions available in the literature. On uniform grids, the method gives second‐order accuracy for both diffusion‐ and convection‐dominated flows. There is little loss of accuracy on grids that are moderately non‐orthogonal. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献