Numerical methods for chemically reacting fluid flow computation under low-Mach number approximation. (English) Zbl 1146.76043

Tokyo J. Math. 29, No. 1, 167-198 (2006); errata 32, No. 2, 559 (2009).
A mathematical model of environmental fluid is presented to describe fluid flow motions with large density variations. Moreover the associated numerical methods are discussed. The model of environmental fluid is formulated as an unsteady low-Mach number flow based on the compressible Navier-Stokes equations. For low-Mach number flows, the acoustic effects are assumed to be weak relative to the advection effects. Under this assumption, detailed acoustic effects can be removed from governing equations. The low-Mach number formulation thus enables numerical flow analysis with a projection methodology that uses high-order accurate upwind difference of the convection terms with a time step restricted solely by an advection Courant-Friedrichs-Lewy (CFL) condition. The algorithm presented here is based on an iterative implicit time evolution of second order accuracy and a high-accurate spatial discretization with TVD properties for unsteady low-Mach number flows. It is seen from the results on the verification for test cases of flows with a wide range of density variations that our numerical method is validated.


76M25 Other numerical methods (fluid mechanics) (MSC2010)
76N15 Gas dynamics (general theory)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76V05 Reaction effects in flows
80A32 Chemically reacting flows
Full Text: DOI DOI


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