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

Abstract A novel 5th-order shock capturing scheme is presented in this paper. The scheme, so-called P 4 T 2 − 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 P 4 T 2 − 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 P 4 T 2 − BVD scheme 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. P 4 T 2 − 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. Highlights • An innovative fifth-order shock capturing scheme is proposed. • Low-dissipation linear scheme is retrieved for smooth solution over all wave numbers. • Discontinuous and smooth solution of wide-band scales are simultaneously solved with high accuracy. • The free-mode solutions are faithfully maintained in long term computation. [ABSTRACT FROM AUTHOR]