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首页> 外文期刊>Journal of Computational Physics >An accurate and robust finite volume scheme based on the spline interpolation for solving the Euler and Navier-Stokes equations on non-uniform curvilinear grids
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An accurate and robust finite volume scheme based on the spline interpolation for solving the Euler and Navier-Stokes equations on non-uniform curvilinear grids

机译：基于样条插值的精确且鲁棒的有限体积方案，用于求解非均匀曲线网格上的Euler和Navier-Stokes方程

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摘要

Spline schemes are proposed to simulate compressible flows on non-uniform structured grid in the framework of finite volume methods. The cubic spline schemes in the present paper can achieve fourth and third order accuracy on the uniform and non-uniform grids respectively. Due to the continuity of cubic spline polynomial function, the inviscid flux can be computed directly from the reconstructed spline polynomial without using the Riemann solvers or other flux splitting techniques. Isotropic and anisotropic artificial viscosity models are introduced to damp high frequency numerical disturbances and to enhance the numerical stability. The first derivatives that are used to calculate the viscous flux are directly obtained from the cubic spline polynomials and preserve second order accuracy on both uniform and non-uniform grids. Ahybrid scheme, in which the spline scheme is blended with shock-capturing WENO scheme, is developed to deal with flow discontinuities. Benchmark test cases of inviscid/viscous flows are presented to demonstrate the accuracy, robustness and efficiency of the proposed schemes. (C) 2015 Elsevier Inc. All rights reserved.
机译：在有限体积方法的框架下，提出了样条方案来模拟非均匀结构网格上的可压缩流。本文的三次样条方案可以分别在均匀网格和非均匀网格上实现四阶和三阶精度。由于三次样条多项式函数的连续性，可以不使用Riemann求解器或其他磁通拆分技术直接从重构的样条多项式计算无粘性通量。引入了各向同性和各向异性的人工粘度模型，以衰减高频数值扰动并增强数值稳定性。从三次样条多项式直接获得用于计算粘性通量的一阶导数，并且在均匀和非均匀网格上均保留二阶精度。开发了一种混合方案，其中将样条方案与捕获冲击的WENO方案相结合，以处理流量不连续性。介绍了无粘性/粘性流的基准测试案例，以证明所提出方案的准确性，鲁棒性和效率。 （C）2015 Elsevier Inc.保留所有权利。

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