A positivity-preserving approach for implicit dual-time stepping schemes in multi-component flow simulations

Abstract

The implicit dual-time stepping schemes are very efficient in solving the multi-component flows with a time scale discrepancy induced by the chemical reactions. However, high-order accurate simulations often fail to obtain a converged result due to non-positive density or pressure during computations. In this paper, we deduce a sufficient condition for positivity-preserving of the dual-time stepping scheme with explicit pseudo-time and implicit physical time stepping, which allows a simple and efficient positivity-preserving flux limiter by the weight average of Lax–Friedrichs and high-order numerical fluxes. This flux limiter requires less time restriction than the earlier positivity-preserving strategy, implying a higher computational efficiency. In addition, it only introduces minor changes in the eigenvalues for the high-order numerical fluxes when projected to conservative variables, retaining the accuracy of the numerical fluxes to the greatest extent possible. This approach can be applied equally to the implicit dual-time stepping scheme because the solution will be positivity-preserving when converged sufficiently. Various validations computed by the fifth-order WENOZ and second-order Runge–Kutta scheme indicate that the present positivity-preserving algorithm possesses an excellent capability of simulating multi-component flows with strong discontinuities accurately and efficiently.