The Random Projection Method for Stiff Detonation Waves

In this paper we present a simple and robust random projection method for underresolved numerical simulation of stii detonation waves in chemically reacting ows. This method is based on the random projection method proposed by the authors for general hyperbolic systems with stii reaction terms 1], where the ignition temperature is randomized in a suitable domain. It is simpliied using the equations of instantaneous reaction, and then extended to handle the interactions of detonations. Extensive numerical experiments, including interaction of detonation waves, and in two dimensions, demonstrate the reliability and robustness of this novel method.

[1]  Weizhu Bao,et al.  Error estimates on the random projection methods for hyperbolic conservation laws with stiff reaction terms , 2002 .

[2]  Matania Ben-Artzi,et al.  The generalized Riemann problem for reactive flows , 1989 .

[3]  Phillip Colella,et al.  Glimm's Method for Gas Dynamics , 1982 .

[4]  Alexandre J. Chorin,et al.  Random choice methods with applications to reacting gas flow , 1977 .

[5]  Richard B. Pember,et al.  Numerical Methods for Hyperbolic Conservation Laws With Stiff Relaxation I. Spurious Solutions , 1993, SIAM J. Appl. Math..

[6]  Myles A. Sussman,et al.  Source term evaluation for combustion modeling , 1993 .

[7]  Andrew J. Majda,et al.  Theoretical and numerical structure for unstable one-dimensional detonations , 1991 .

[8]  P. Colella,et al.  Theoretical and numerical structure for reacting shock waves , 1986 .

[9]  H. C. Yee,et al.  Numerical wave propagation in an advection equation with a nonlinear source term , 1992 .

[10]  J. Glimm.  Solutions in the large for nonlinear hyperbolic systems of equations , 1965 .

[11]  Randall J. LeVeque,et al.  A Modified Fractional Step Method for the Accurate Approximation of Detonation Waves , 2000, SIAM J. Sci. Comput..

[12]  M. Lighthill.  Supersonic Flow and Shock Waves , 1949, Nature.

[13]  Z. Xin,et al.  The relaxation schemes for systems of conservation laws in arbitrary space dimensions , 1995 .

[14]  Randall J. LeVeque,et al.  A study of numerical methods for hyperbolic conservation laws with stiff source terms , 1990 .

[15]  Ronald Fedkiw,et al.  Numerical resolution of pulsating detonation waves , 2000 .