Hybrid high-resolution RBF-ENO method

被引：1

作者：

Hesthaven J.S. ^{[1
]}

Mönkeberg F. ^{[1
]}

机构：

[1] SB-MATH-MCSS, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne

来源：

Journal of Computational Physics: X | 2021年 / 12卷

关键词：

Conical aerospike nozzle; ENO reconstruction; Finite volume method; Hybrid grids; Positivity preserving method; Radial basis functions;

D O I：

10.1016/j.jcpx.2021.100089

中图分类号：

学科分类号：

摘要：

Essentially nonoscillatory (ENO) and weighted ENO (WENO) methods on equidistant Cartesian grids are widely used to solve partial differential equations with discontinuous solutions. The RBF-ENO method is highly flexible in terms of geometry, but its stencil selection algorithm is computational expensive. In this work, we combine the computationally efficient WENO method and the geometrically flexible RBF-ENO method in a hybrid high-resolution essentially nonoscillatory method to solve hyperbolic conservation laws. The scheme is based on overlapping patches with ghost cells, the RBF-ENO method for unstructured patches and a standard WENO method on structured patches. Furthermore, we introduce a positivity preserving limiter for non-polynomial reconstruction methods to stabilize the hybrid RBF-ENO method for problems with low density or pressure. We show its robustness and flexibility on benchmarks and complex test cases such as the scramjet inflow problem and a conical aerospike nozzle jet simulation. © 2021 The Authors

引用

共 59 条

[1]

Gottlieb S., Ketcheson D.I., Shu C.-W., High order strong stability preserving time discretizations, J. Sci. Comput., 38, pp. 251-289, (2009)

[2]

Van Leer B., Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method, J. Comput. Phys., 32, pp. 101-136, (1979)

[3]

Lanczos C., Discourse on Fourier Series, Vol. 76, (2016)

[4]

Harten A., Engquist B., Osher S., Chakravarthy S.R., Uniformly high order accurate essentially non-oscillatory schemes, III, J. Comput. Phys., 71, pp. 231-303, (1987)

[5]

Harten A., Chakravarthy S.R., Multi-dimensional ENO schemes for general geometries, (1991)

[6]

Abgrall R., On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation, J. Comput. Phys., 114, pp. 45-58, (1994)

[7]

Liu X.-D., Osher S., Chan T., Weighted essentially non-oscillatory schemes, J. Comput. Phys., 115, pp. 200-212, (1994)

[8]

Hardy R.L., Multiquadric equations of topography and other irregular surfaces, J. Geophys. Res., 76, pp. 1905-1915, (1971)

[9]

Iske A., Approximation Theory and Algorithms for Data Analysis, (2018)

[10]

Buhmann M.D., Radial basis functions, Acta Numer., 2000, 9, pp. 1-38, (2000)

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