We present, for the SUPG formulation of inviscid compressible flows, stabilization parameters defined based on the degree-of-freedom submatrices of the element-level matrices. With 2D steady-state test problems involving supersonic flows and shocks, we compare these stabilization parameters with the ones defined based on the full element-level matrices. We also compare them to the stabilization parameters introduced in the earlier development stages of the SUPG formulation of compressible flows. In all cases the formulation includes a shock-capturing term involving a shockcapturing parameter. We investigate the difference between updating the stabilization and shock-capturing parameters at the end of every time step and at the end of every nonlinear iteration within a time step. The formulation includes, as an option, an algorithmic feature that is based on freezing the shock-capturing parameter at its current value when a convergence stagnation is detected.
SUMMARYWe present, for the SUPG formulation of inviscid compressible ows with shocks, stabilization parameters deÿned based on the element-level matrices. These deÿnitions are expressed in terms of the ratios of the norms of the matrices and take into account the ow ÿeld, the local length scales, and the time step size. Calculations of these stabilization parameters are straightforward and do not require explicit expressions for length or velocity scales. We compare the performance of these stabilization parameters, accompanied by a shock-capturing parameter introduced earlier, with the performance of a stabilization parameter introduced earlier, accompanied by the same shock-capturing parameter. We investigate the performance di erence between updating the stabilization and shock-capturing parameters at the end of every time step and at the end of every non-linear iteration within a time step. We also investigate the in uence of activating an algorithmic option that was introduced earlier, which is based on freezing the shock-capturing parameter at its current value when a convergence stagnation is detected.
SUMMARYA procedure to improve convergence towards steady state in inviscid ow simulations is presented. This procedure detects convergence stagnation as the solution progresses, and freezes the shock-capturing term of an implicit, semi-discrete SUPG ÿnite element formulation in conservation variables with local timestepping. Numerical experiments show that machine zero solutions are obtained with a small number of time steps, without loss of accuracy.
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