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Positivity-preserving time discretizations for production-destruction equations with applications to non-equilibrium flows. (English) Zbl 1420.35190
Summary: In this paper, we construct a family of modified Patankar Runge-Kutta methods, which is conservative and unconditionally positivity-preserving, for production-destruction equations, and derive necessary and sufficient conditions to obtain second-order accuracy. This ordinary differential equation solver is then extended to solve a class of semi-discrete schemes for PDEs. Combining this time integration method with the positivity-preserving finite difference weighted essentially non-oscillatory (WENO) schemes, we successfully obtain a positivity-preserving WENO scheme for non-equilibrium flows. Various numerical tests are reported to demonstrate the effectiveness of the methods.

35Q30 Navier-Stokes equations
76V05 Reaction effects in flows
76N99 Compressible fluids and gas dynamics
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
Full Text: DOI
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