Adaptive Osher-type scheme for the Euler equations with highly nonlinear equations of state
Adaptive Osher-type scheme for the Euler equations with highly nonlinear equations of state
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DOI：
10.1016/j.jcp.2013.03.046
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发表时间：
2013-08
期刊：
影响因子：
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通讯作者：
B. Lee;E. Toro;C. Castro;N. Nikiforakis
中科院分区：
文献类型：
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作者：
B. Lee;E. Toro;C. Castro;N. Nikiforakis
在凝聚态炸药爆震数值模拟中，常用的是复杂状态方程，如Jones-Wilkins-Lee （JWL）方程和Cochran-Chan （C-C）方程。然而，当使用保守格式求解具有这种状态方程的欧拉方程时，即使对于单一材料，也会出现跨接触不连续的伪解，这是多流体系统中众所周知的现象。在这项工作中，我们在自适应原始-保守框架中开发了一种广义的osher型方案来克服上述困难。将所得数值解与精确解进行比较，并与Godunov方法结合精确黎曼解对具有mie - grgrneisen状态方程形式的欧拉方程（如JWL和C-C状态方程）的数值解进行比较。将自适应方案推广到二阶，给出了其经验收敛速率，验证了其二阶光滑解的精度。通过一系列一维和二维空间的测试问题，我们说明了保守格式的失败以及本文方法克服这些困难的能力。
For the numerical simulation of detonation of condensed phase explosives, a complex equation of state (EOS), such as the Jones–Wilkins–Lee (JWL) EOS or the Cochran–Chan (C–C) EOS, are widely used. However, when a conservative scheme is used for solving the Euler equations with such equations of state, a spurious solution across the contact discontinuity, a well known phenomenon in multi-fluid systems, arises even for single materials. In this work, we develop a generalised Osher-type scheme in an adaptive primitive–conservative framework to overcome the aforementioned difficulties. Resulting numerical solutions are compared with the exact solutions and with the numerical solutions from the Godunov method in conjunction with the exact Riemann solver for the Euler equations with Mie–Grüneisen form of equations of state, such as the JWL and the C–C equations of state. The adaptive scheme is extended to second order and its empirical convergence rates are presented, verifying second order accuracy for smooth solutions. Through a suite of several tests problems in one and two space dimensions we illustrate the failure of conservative schemes and the capability of the methods of this paper to overcome the difficulties.