Second-order Godunov-type scheme for reactive flow calculations on moving meshes
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Aims. In this paper, we present a new method to perform numerical simulations of astrophysical MHD flows using the Adaptive Mesh Refinement framework and Constrained Transport.
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Higher-order versions of Godunov's method have proven highly successful for high-Mach-number compressible flow. One goal of the research being described in this paper is to extend the range of applicability of these methods to more general systems of hyperbolic conversion laws such as magnetohydrodynamics, flow in porous media and finite deformations of elastic-plastics solids. A second goal is to apply Godunov methods to problems involving more complex physical and solution geometries than can be treated on a simple rectangular grid. This requires the introduction of various adaptive methodologies: global moving and body-fitted meshes, local adaptive mesh refinement, and front tracking. 11 refs., 6 figs.
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Abstract 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.
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We extend the unified coordinate system proposed by Hui et al.to axisymmetric Euler equations.The form and hyperbolicity of axisymmetric Euler equations are discussed.Solution of 1-D Riemann problem solved by axisymmetric Euler equations after dimensional splitting is shown.Axisymmetric Euler equations are numerically solved using Godunov scheme with MUSCL update.Numerical results show advantages of unified coordinates.
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This paper describes an adaptive mesh refinement algorithm for unsteady gas dynamics. The algorithm is based on an unsplit, second-order Godunov integration scheme for logically-rectangular moving quadrilateral grids. The integration scheme is conservative and provides a robust, high resolution discretization of the equations of gas dynamics for problems with strong nonlinearities. The integration scheme is coupled to a local adaptive mesh refinement algorithm that dynamically adjusts the location of refined grid patches to preserve the accuracy of the solution, preserving conservation at interfaces between coarse and fine grids while adjusting the geometry of the fine grids so that grid lines remain smooth under refinement. Numerical results are presented illustrating the performance of the algorithm. 5 refs., 3 figs.
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