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首页> 外文期刊>Journal of Computational Physics >IMPROVED SOLUTIONS TO THE SMALL STRAIN CONTINUUM EQUATIONS USING A MODIFIED ENGQUIST FILTER
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IMPROVED SOLUTIONS TO THE SMALL STRAIN CONTINUUM EQUATIONS USING A MODIFIED ENGQUIST FILTER

机译：使用改进的Enquist滤波器改进小应变连续方程的解决方案

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摘要

For wave propagation problems in linear and bilinear elastic solids and a class of simple nonlinear solids the benefits of high-resolution schemes in gasdynamics can be immediately extended to solid mechanics. The Engquist filter for the system of conservation laws in gasdynamics is extended to solid mechanics and implemented in a finite-difference code. The present results show that highly resolved numerical solutions, i.e., sharp shocks with very little oscillation behind them, can be achieved by applying this nonlinear filter to the finite-difference solution at every timestep. Plane wave propagation in three types of solids is calculated by the LAYER code. A two-dimensional grid is used to compute these one-dimensional plane wave problems. For linear elastic solids the nonlinear filter performed very well in removing the Gibbs oscillations. For bilinear solids the numerical solution is compared to a known analytical solution. Because this analytical solution involves a planar shock with a decaying pressure behind it, the existing form of the Engquist filter (designed for a constant pressure behind the shock) has to be modified. The relationship between this modified filter and the flux modification in the TVD scheme is discussed. This modification is expected to be necessary when the filler is applied to multidimensional problems. The potential for obtaining highly resolved shocks from classical second-order finite-difference solid mechanics codes using the modified nonlinear filter is demonstrated. (C) 1996 Academic Press, Inc. [References: 13]
机译：对于线性和双线性弹性固体中的波传播问题以及一类简单的非线性固体，气体动力学中高分辨率方案的优势可以立即扩展到固体力学。用于气体动力学守恒定律系统的Engquist滤波器扩展到固体力学，并以有限差分代码实现。目前的结果表明，通过在每个时间步长上将此非线性滤波器应用于有限差分解决方案，可以实现高度解析的数值解决方案，即在其后几乎没有振荡的剧烈冲击。平面波在三种类型的固体中的传播是通过LAYER代码计算的。二维网格用于计算这些一维平面波问题。对于线性弹性固体，非线性滤波器在消除吉布斯振动方面表现非常出色。对于双线性固体，将数值解与已知的解析解进行比较。由于此分析解决方案涉及平面冲击，其后具有衰减压力，因此必须修改现有形式的Engquist过滤器（设计用于冲击后的恒定压力）。讨论了该修改滤波器与TVD方案中通量修改之间的关系。当将填料应用于多维问题时，预计需要进行这种修改。演示了使用改进的非线性滤波器从经典的二阶有限差分固体力学代码获得高度解析的冲击的潜力。 （C）1996 Academic Press，Inc. [参考：13]

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