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We present, for the SUPG formulation of inviscid compressible flows with shocks, stabilization parameters defined based on the element-level matrices. These definitions are expressed in terms of the ratios of the norms of the matrices and take into account the flow field, 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 difference 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 influence 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. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A stabilization technique targeting the Reynolds-averaged Navier-Stokes (RANS) equations is proposed to account for the multiscale nature of turbulence and high solution gradients. The objective is effective stabilization in computations with the advection- diffusion reaction equations, which are typical of the class of turbulence scale-determining equations where reaction-dominated effects strongly influence the boundary layer prediction in the presence of nonequilibrium phenomena. The stabilization technique, which is based on a variational multiscale method, includes a discontinuity-capturing term designed to be operative when the solution gradients are high and the reactionlike terms are dominant. As test problems, we use a 2D model problem and 3D flow computation for a linear compressor cascade. [ABSTRACT FROM AUTHOR]