Improvement and Numerical Verification of Weighting Strategy for High Precision WCNS Scheme

Abstract

In order to reveal the complex flow mechanism, a series of high-order precision schemes have been proposed at home and abroad, of which, the weighted compact nonlinear scheme (WCNS) has a good shock capture ability and has been widely used in the numerical simulation of complex flows. However, it has insufficient resolution and large dissipation in the simulation of small-scale flows. In the framework of the WCNS, by using the weighting strategy of the targeted essentially non-oscillatory (TENO) scheme for reference, this paper introduces the new methods of discontinuity detection and template weighting into the construction of the WCNS scheme, and develops a WCNS7-T scheme with a 7-order accuracy. Example tests are conducted through one-dimensional shock tube problem and two-dimensional Riemann problem. By comparing with the traditional WCNS7-Z scheme, the improved performance of the new scheme is verified. The numerical experiments show that the WCNS7-T scheme can better suppress the numerical oscillation near the discontinuity, improve the resolution and shock capture ability, and further reduce the dissipation.

Keywords

• compressible flow
• high precision scheme
• shock discontinuity
• nonlinear weighting