A fifth-order shock capturing scheme with two-stage boundary variation diminishing algorithm

被引:66
作者
Deng, Xi [1 ]
Shimizu, Yuya [1 ]
Xiao, Feng [1 ]
机构
[1] Tokyo Inst Technol, Dept Mech Engn, Meguro Ku, 2-12-1 Ookayama, Tokyo 1528550, Japan
基金
日本学术振兴会;
关键词
Shock capturing; High order schemes; Boundary variation diminishing; THINC scheme; Hyperbolic systems; ESSENTIALLY NONOSCILLATORY SCHEMES; HIGH-RESOLUTION SCHEMES; VOLUME WENO SCHEMES; HIGH-ORDER; EFFICIENT IMPLEMENTATION; FINITE-DIFFERENCE; UNSTRUCTURED GRIDS; RIEMANN PROBLEM; THINC METHOD; RECONSTRUCTION;
D O I
10.1016/j.jcp.2019.02.024
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
A novel 5th-order shock capturing scheme is presented in this paper. The scheme, so-called P4T2 - BVD (polynomial of 4-degree and THINC function of 2-level reconstruction based on BVD algorithm), is formulated as a two-stage spatial reconstruction scheme following the BVD (Boundary Variation Diminishing) principle that minimizes the jumps of the reconstructed values at cell boundaries. In the P4T2 - BVD scheme, polynomial of degree four and THINC (Tangent of Hyperbola for INterface Capturing) functions with two-level steepness are used as the candidate reconstruction functions. The final reconstruction function is selected through the two-stage BVD algorithm so as to effectively control both numerical oscillation and dissipation. Spectral analysis and numerical verifications show that the P4T2 - BVDscheme possesses the following desirable properties: 1) it effectively suppresses spurious numerical oscillation in the presence of strong shock or discontinuity; 2) it substantially reduces numerical dissipation errors; 3) it automatically retrieves the underlying linear 5th-order upwind scheme for smooth solution over all wave numbers; 4) it is able to resolve both smooth and discontinuous flow structures of all scales with substantially improved solution quality in comparison to other existing methods; and 5) it produces accurate solutions in long term computation. P4T2 - BVD, as well as the underlying idea presented in this paper, provides an innovative and practical approach to design high-fidelity numerical schemes for compressible flows involving strong discontinuities and flow structures of wide range scales. (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页码:323 / 349
页数:27
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