A Split Random Time Stepping Method for Stiff and Non-stiff Chemically Reacting Flows

TL;DR

This paper introduces a novel split random time stepping method for simulating both stiff and non-stiff chemically reacting flows, aiming to improve accuracy and robustness in capturing discontinuities and reaction dynamics.

Contribution

The study proposes a new fractional step method that employs random reaction activation/deactivation to address numerical issues in stiff and non-stiff reacting flows, extending previous random projection techniques.

Findings

Effective correction of discontinuity propagation errors.

Robust performance in stiff and non-stiff flow simulations.

Recovers standard results in nonstiff cases with fine resolution.

Abstract

In this paper, a new fractional step method is proposed for simulating stiff and nonstiff chemically reacting flows. In stiff cases, a well-known spurious numerical phenomenon, i.e. the incorrect propagation speed of discontinuities, may be produced by general fractional step methods due to the under-resolved discretization in both space and time. The previous random projection method has been successfully applied for stiff detonation capturing in under-resolved conditions. Not to randomly project the intermediate state into two presumed equilibrium states (completely burnt or unburnt) as in the random projection method, the present study is to randomly choose the time-dependent advance or stop of a reaction process. Each one-way reaction has been decoupled from the multi-reaction kinetics using operator splitting and the local smeared temperature due to numerical dissipation of shock-capturing schemes is compared with a random one within two limited temperatures corresponding to the advance and its inverse states, respectively, to control the random reaction. The random activation or deactivation in the reaction step is thus promising to correct the deterministic accumulative error of the propagation of discontinuities. Extensive numerical experiments, including model problems and realistic reacting flows in one and two dimensions, demonstrate this expectation as well as the effectiveness and robustness of the method. Meanwhile, for nonstiff problems when spatial and temporal resolutions are fine, the proposed random method recovers the results as general fractional step methods, owing to the increasing possibility of activation with diminishing randomness by adding a shift term.