Abstract: A popular approach to numerical simulation of unsteady flow problems are flux-corrected transport (FCT) algorithms which are capable of producing accurate solutions without numerical artifacts such as non-physical oscillations in the vicinity of step gradients. In the first part of this talk, the design of algebraic flux correction (AFC) finite element schemes is revisited in the context of the compressible Euler equations of gas dynamics. A new synchronized FCT algorithm is presented which ensures that all selected quantities of interest (density, energy, pressure, velocity) are bounded by the values of their low-order counterparts. To this end, the fully multidimensional FCT flux limiter is applied to a set of indicator quantities, whereby a node-based transformation from the conservative to the primitive variables is performed. To reduce the computational costs of the FCT algorithm, the raw antidiffusive fluxes are linearized about an auxiliary state, so that the solution-dependent correction factors need to be computed just once per time step. Moreover, flux limiting reduces to a simple post-processing of the converged low-order solution. It can therefore be equipped with a simple failsafe strategy which ensures that the flux-corrected end-of-step solution is still bounded by its low-order values. In the second part of the talk, the presented techniques are applied to an idealized Z-pinch implosion model recently proposed by J.W. Banks and J.N. Shadid. It is based on the compressible Euler equations which include a magnetic source term and are coupled with a scalar tracer equation. The synchronized flux limiting procedure is shown to produce promising results for this challenging problem.
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