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首页> 外文期刊>Journal of Computational Physics >An Eulerian-Lagrangian WENO finite volume scheme for advection problems
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An Eulerian-Lagrangian WENO finite volume scheme for advection problems

机译：对流问题的欧拉-拉格朗日WENO有限体积格式

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摘要

We develop a locally conservative Eulerian-Lagrangian finite volume scheme with the weighted essentially non-oscillatory property (EL-WENO) in one-space dimension. This method has the advantages of both WENO and Eulerian-Lagrangian schemes. It is formally high-order accurate in space (we present the fifth order version) and essentially non-oscillatory. Moreover, it is free of a CFL time step stability restriction and has small time truncation error. The scheme requires a new integral-based WENO reconstruction to handle trace-back integration. A Strang splitting algorithm is presented for higher-dimensional problems, using both the new integral-based and pointwise-based WENO reconstructions. We show formally that it maintains the fifth order accuracy. It is also locally mass conservative. Numerical results are provided to illustrate the performance of the scheme and verify its formal accuracy.
机译：我们开发了一种局部保守的欧拉-拉格朗日有限体积方案，在一个空间维度上具有加权的基本非振荡性质（EL-WENO）。该方法具有WENO和Eulerian-Lagrangian方案的优点。它在空间上形式上是高阶准确的（我们提供了五阶形式），并且基本上是无振荡的。此外，它不受CFL时间步长稳定性的限制，并且时间截断误差小。该方案需要新的基于积分的WENO重构来处理回溯集成。使用新的基于积分和基于点的WENO重构，提出了针对高维问题的Strang分裂算法。我们正式表明它保持了五阶精度。它也是当地群众保守的。提供数值结果以说明该方案的性能并验证其形式准确性。

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