DETONATION CAPTURING FOR STIFF COMBUSTION CHEMISTRY

This paper contributes to the topic of unphysical one-cell-per-time-st ep travelling combustion wave solutions in numerical computations of d etonation waves in the presence of stiff chemical source terms. These false weak detonation solutions appear when a gasdynamics-chemistry op erator-splitting technique is used in conjunction with modem shock-cap turing schemes for compressible Bow simulations. A detailed analysis o f piecewise constant three-state weak solutions of the Fickett-Majda d etonation model equations is carried out. These structures are idealiz ed analogues of the fake numerical solutions observed in computations. The analysis suggests that the problem can be cured by introducing a suitable ignition temperature below which the chemistry is frozen. It is found that the threshold temperatures needed to effectively suppres s the undesired numerical artefacts are considerably lower than any te mperature actually found in the reaction zone of a resolved detonation . This is in contrast to earlier suggestions along the same lines in t he literature and it allows us to propose the introduction of such a l ow and otherwise irrelevant ignition temperature threshold as a routin e measure for overcoming the problem of artificial weak detonations. T he criterion for choosing the ignition temperature is then extended to the reactive Euler equations and extensive computational tests for bo th the model and the full equations demonstrate the effectiveness of o ur strategy. We consider the behaviour of a first-order Godunov-type s cheme as well as its second-order extension in space and time using va n Leer's MUSCL approach and Strang splitting.