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Finite element solution of compressible viscous flows using conservative variables. (English) Zbl 0848.76039

Summary: A finite element method for solving the compressible Navier-Stokes equations is presented. These equations are solved in conservation form and using conservative variables. Appropriate finite element approximations are discussed when a Galerkin variational formulation is used. For high-speed flows, the formulation is stabilized using the stream line upwind Petrov-Galerkin method for which we propose in analytical expression for the matrix \(\tau\). A new discontinuity-capturing operator is also proposed to accurately solve flow problems exhibiting sharp gradients. The nonlinear systems of equations arising from the discretization are solved using an iterative strategy based on the generalized minimal residual (GMRES) algorithm. Numerical results for transonic and supersonic flows are presented that demonstrate the effectiveness of the proposed method.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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