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A preconditioning mass matrix to accelerate the convergence to the steady Euler solutions using explicit schemes. (English) Zbl 0772.76054

The authors present, with analytical and numerical results, how the use of a preconditioning mass matrix (PMM) accelerates the convergence in a prescribed range of Mach numbers. It has been also claimed that PMM can be applied to any FEM/FVM that uses an explicit time marching scheme to find the steady state. The rate of convergence to the steady state is also studied and the results for the one- and two-dimensional cases are presented. Finally, it is concluded that the numerical scheme presented is very efficient in terms of computing time, simplicity in programming and is also as robust as the original scheme.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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