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首页> 外文期刊>Journal of Computational Physics >A high order moving boundary treatment for compressible inviscid flows
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A high order moving boundary treatment for compressible inviscid flows

机译：可压缩无粘性流的高阶运动边界处理

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摘要

We develop a high order numerical boundary condition for compressible inviscid flows involving complex moving geometries. It is based on finite difference methods on fixed Cartesian meshes which pose a challenge that the moving boundaries intersect the grid lines in an arbitrary fashion. Our method is an extension of the so-called inverse Lax-Wendroff procedure proposed in [17] for conservation laws in static geometries. This procedure helps us obtain normal spatial derivatives at inflow boundaries from Lagrangian time derivatives and tangential derivatives by repeated use of the Euler equations. Together with high order extrapolation at outflow boundaries, we can impose accurate values of ghost points near the boundaries by a Taylor expansion. To maintain high order accuracy in time, we need some special time matching technique at the two intermediate Runge-Kutta stages. Numerical examples in one and two dimensions show that our boundary treatment is high order accurate for problems with smooth solutions. Our method also performs well for problems involving interactions between shocks and moving rigid bodies.
机译：我们为涉及复杂移动几何体的可压缩无粘性流开发了一个高阶数值边界条件。它基于固定笛卡尔网格上的有限差分方法，这带来了一个挑战，即移动边界以任意方式与网格线相交。我们的方法是[17]中提出的所谓静态Lax-Wendroff逆过程的扩展，用于静态几何中的守恒律。此过程可帮助我们通过重复使用欧拉方程，从拉格朗日时间导数和切向导数获得流入边界处的法向空间导数。结合流出边界处的高阶外推，我们可以通过泰勒展开在边界附近施加精确的幻影点值。为了保持较高的时间精度，我们需要在两个中间的Runge-Kutta阶段使用一些特殊的时间匹配技术。一维和二维数值例子表明，对于光滑解的问题，我们的边界处理是高阶准确的。对于涉及冲击和运动刚体之间相互作用的问题，我们的方法也表现良好。

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