The dual information preserving method for stiff reacting flows

Abstract

In this paper, we construct a new numerical method to solve the reactive Euler equations to cure the numerical stiffness problem. The species mass equations are first decoupled from the reactive Euler equations, and then they are further fractionated into the convection step and the reaction step. In the convection step, by introducing two kinds of Lagrangian points (cell-point and particle-point), a dual information preserving (DIP) method is proposed to resolve the convection characteristics. In this new method, the information (including the transport value and the relative coordinates to the center of the current cell) of the cell-point and that of the particle-point are updated according to the velocity field. The information of the cell-point in a cell can effectively restrict the incorrect reaction activation caused by the numerical dissipation, while the information of the particle-point can help to preserve the sharp shock front once the strong shock waves are formed. Hence, by using the DIP method, the spurious numerical propagation phenomenon in stiff reacting flows is effectively eliminated. In addition, a numerical perturbation method is also developed to solve the fractional reaction step (ODE equation) to improve the stability and efficiency. A series of numerical examples are presented to validate the accuracy and robustness of the new method.