Implicit space-time residual distribution method for unsteady laminar viscous flow

The solution is obtained at each time-step by solving an implicit non-linear system of equations. Here, following [Int. J. Numer. Methods Fluids 40 (2002) 573; Á.G. Csı́k, Upwind residual distribution schemes for general hyperbolic conservation laws and application to ideal magnetohydrodynamics, PhD thesis, Katholieke Universiteit Leuven, 2002], we formulate the solution of this system as a steady state problem in a pseudo-time variable. We discuss the efficiency of an explicit Euler forward pseudo-time integrator compared to the implicit Euler. When applied to viscous computation, the implicit method has shown speed-ups of more than a factor 50 in terms of computational time.