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首页> 外文期刊>SIAM Journal on Numerical Analysis >Time-implicit approximation of the multipressure gas dynamics equations in several space dimensions
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Time-implicit approximation of the multipressure gas dynamics equations in several space dimensions

机译：在多个空间维中的多压力气体动力学方程的时间隐式近似

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摘要

The present work is devoted to the numerical approximation of the solutions of the inviscid limit of multipressure Navier-Stokes equations in several space dimensions. The nonconservation form of the Euler-like limit model makes the shock solutions sensitive with respect to the underlying small scales and then challenges their numerical approximation. In particular, classical algorithms fail in producing good numerical results. Here we are mainly concerned with (large time stepping) implicit numerical strategies. We first exhibit a set of generalized jump conditions satisfied by the shock solutions and well-suited to derive a time-implicit scheme. We then devise a linearized time-implicit solver for the sake of efficiency. This solver is shown to preserve the positivity of each internal energy εi provided that the total internal energy stays positive.
机译：本工作致力于在多个空间维度上对多压力Navier-Stokes方程的无粘性极限的解进行数值逼近。欧拉式极限模型的非守恒形式使激波解相对于底层小尺度敏感，然后挑战其数值逼近。特别是，经典算法无法产生良好的数值结果。在这里，我们主要关注（大量时间步进）隐式数值策略。我们首先展示了一组由冲击解满足的广义跳跃条件，非常适合推导时间隐式方案。然后，出于效率考虑，我们设计了线性化时间隐式求解器。只要总内部能量保持正值，该求解器将保持每个内部能量εi的正值。

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