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Journal of Scientific Computing

Erschienen in:

01.10.2020

Compact Schemes for Multiscale Flows with Cell-Centered Finite Difference Method

verfasst von: Yao Jin, Fei Liao, Jinsheng Cai

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2020

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Abstract

High-order compact interpolation schemes appropriate for multiscale flows are studied within a cell-centered finite difference method (CCFDM) framework where the robustness of high-order schemes on curvilinear grids can be greatly enhanced due to the satisfaction of geometric conservation law. Two types of compact interpolations are mainly developed in this paper for shock-free flows and shock-embedded flows respectively. The present compact schemes are verified to be superior over the explicit counterparts with same orders in terms of the spectral characteristics. Regarding the shock-free flows, low-dissipation low-dispersion properties are achieved by the spectral optimization. Three optimized compact schemes (Opt4, Opt6 and Opt8) are further validated to be attractive for shock-free problems by carrying out benchmarks from computational aeroacoustics workshops and two typical turbulence cases: Tayler–Green vortex and decaying isotropic turbulence. Regarding high-speed flows in the presence of shock waves, the shock-capturing capability is realized by extending the weighting technique to the compact interpolations. The criteria to choose optimally compact nonlinear sub-stencils on a most general compact global stencil are presented. Interestingly, the explicit WENO-type schemes can be reverted within the proposed compact framework. Three nonlinear compact schemes (UI5, CI6 and CI8) on two practical stencils are analyzed and further compared with their explicit counterparts by a series of numerical experiments. The compact ones are superior to explicit ones in resolving rich flow structures as well as discontinuities.

Vorheriger Artikel A New Projection-Based Stabilized Virtual Element Method for the Stokes Problem

Nächster Artikel A New Method for Solving Variational Inequalities and Fixed Points Problems of Demi-Contractive Mappings in Hilbert Spaces

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Titel: Compact Schemes for Multiscale Flows with Cell-Centered Finite Difference Method
verfasst von: Yao Jin
Fei Liao
Jinsheng Cai
Publikationsdatum: 01.10.2020
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2020
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01314-w

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