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    IMPLICIT RELAXED ALL MACH NUMBER SCHEMES FOR GASES AND COMPRESSIBLE MATERIALS

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    We present an implicit relaxation scheme for the simulation of compressible flows in all Mach number regimes based on a Jin–Xin relaxation approach. The main features of the proposed scheme lie in its simplicity and effectiveness. Thanks to the linearity of the flux in the relaxation system, the time semidiscrete scheme can be reformulated in linear decoupled elliptic equations resulting in the same number of unknowns as in the original system. To obtain the correct numerical diffusion in all Mach number regimes, a convex combination of upwind and centered fluxes is applied. The numerical scheme is validated by applying it on a model for nonlinear elasticity. Simulations of gas and fluid flows, as well as deformations of compressible solids are carried out to assess the performance of the numerical scheme in accurately approximating material waves in different Mach regimes

    Feedback control by low-order modelling of the laminar flow past a bluff body

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    In this work a two-dimensional laminar flow past a square cylinder is considered. Actuators placed on the cylinder enable active control by blowing and suction. Proportional feedback control is then applied using velocity measurements taken in the cylinder wake. Projection onto an empirical subspace is combined with a calibration technique to build a low-order model of the incompressible Navier–Stokes equations. This model is used within an optimization method to determine a set of feedback gains which reduces the unsteadiness of the wake at Re =150. The resulting controlled flows are further characterized by computing the critical Reynolds numbers for the onset of the vortex shedding instability
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