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首页> 外文期刊>Journal of Computational Physics >Positivity-preserving Lagrangian scheme for multi-material compressible flow
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Positivity-preserving Lagrangian scheme for multi-material compressible flow

机译：多材料可压缩流的保正拉格朗日格式

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摘要

Robustness of numerical methods has attracted an increasing interest in the community of computational fluid dynamics. One mathematical aspect of robustness for numerical methods is the positivity-preserving property. At high Mach numbers or for flows near vacuum, solving the conservative Euler equations may generate negative density or internal energy numerically, which may lead to nonlinear instability and crash of the code. This difficulty is particularly profound for high order methods, for multi-material flows and for problems with moving meshes, such as the Lagrangian methods. In this paper, we construct both first order and uniformly high order accurate conservative Lagrangian schemes which preserve positivity of physically positive variables such as density and internal energy in the simulation of compressible multi-material flows with general equations of state (EOS). We first develop a positivity-preserving approximate Riemann solver for the Lagrangian scheme solving compressible Euler equations with both ideal and non-ideal EOS. Then we design a class of high order positivity-preserving and conservative Lagrangian schemes by using the essentially non-oscillatory (ENO) reconstruction, the strong stability preserving (SSP) high order time discretizations and the positivity-preserving scaling limiter which can be proven to maintain conservation and uniformly high order accuracy and is easy to implement. One-dimensional and two-dimensional numerical tests for the positivity- preserving Lagrangian schemes are provided to demonstrate the effectiveness of these methods.
机译：数值方法的鲁棒性引起了人们对计算流体动力学界的越来越多的关注。数值方法鲁棒性的一个数学方面是保持正性。在高马赫数或接近真空的流量下，求解保守的欧拉方程可能会在数值上产生负密度或内部能量，这可能会导致非线性不稳定和代码崩溃。对于高阶方法，多材料流以及移动网格的问题（例如拉格朗日方法），此困难尤其严重。在本文中，我们构造了一阶和一致高阶精确保守Lagrangian方案，这些方案在物理状态方程（EOS）的可压缩多材料流模拟中保留了物理正变量（例如密度和内能）的正值。我们首先为拉格朗日方案开发一个保正近似Riemann求解器，用于求解具有理想和非理想EOS的可压缩Euler方程。然后，我们通过使用本质上非振荡（ENO）重构，强稳定性保持（SSP）高阶时间离散化和保持阳性的比例限制器，设计了一类保持高阶阳性的保守Lagrangian方案。保持节约和统一的高阶精度，并且易于实现。提供了保留正拉格朗日方案的一维和二维数值测试，以证明这些方法的有效性。

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