Unsplit algorithms for multidimensional systems of hyperbolic conservation laws with source terms
This work describes an unsplit, second-order accurate algorithm for multidimensional systems of hyperbolic conservation laws with source terms, such as the compressible Euler equations for reacting flows. It is a MUSCL-type, shock-capturing scheme that integrates all terms of the governing equations simultaneously, in a single time-step, thus avoiding dimensional or time-splitting. Appropriate families of space-time manifolds are introduced, along which the conservation equations decouple to the characteristic equations of the corresponding 1-D homogeneous system. The local geometry of these manifolds depends on the source terms and the spatial derivatives of the flow variables. Numerical integration of the characteristic equations is performed along these manifolds in the upwinding part of the algorithm. Numerical simulations of two-dimensional detonations with simplified kinetics are performed to test the accuracy and robustness of the algorithm. These flows are unstable for a wide range of parameters and may exhibit chaotic behavior. Grid-convergence studies and comparisons with earlier results, obtained with traditional schemes, are presented.
© 2002 Elsevier Science. Received June 2001; revised and accepted September 2001. This work is sponsored by the Air Force Office of Scientific Research Grant No. F49620-94-1-0353 and F49626-93-1-00338, whose support is gratefully acknowledged.
Published - Papalexandris_LD.2002.CMA.pdf