Second Order Unconditional Positive Preserving Schemes for Non-equilibrium Reactive Flows with Mass and Mole Balance

TL;DR

This paper introduces second order positive-preserving schemes for non-equilibrium reactive flows that maintain mass and mole balance, ensuring positivity of density and pressure, and are validated through accuracy and benchmark tests.

Contribution

It develops a novel family of second order modified Patankar Runge-Kutta schemes that preserve positivity and balance in reactive flow simulations.

Findings

Schemes maintain positivity of density and pressure.

Achieve the expected order of accuracy.

Validated through benchmark tests.

Abstract

In this study, a family of second order process based modified Patankar Runge-Kutta schemes is proposed with both the mass and mole maintained in balance while preserving the positivity of density and pressure with the time step determined by convection terms. The accuracy analysis is conducted to derive the sufficient and necessary conditions for the Runge-Kutta and Patankar coefficients. Coupling with the finite volume method, the proposed schemes are extended to Euler equations with non-equilibrium reacting source terms. Benchmark tests are given to prove the prior order of accuracy and validate the positive-preserving property for both density and pressure.