Space adaptive methods with error control based on adaptive multiresolution for incompressible flows (Marc-Arthur N'Guessan, Ecole Polytechnique)

25.02.2020 14:00

We address the development of new numerical methods for the efficient resolution of stiff Partial Differential Equations modelling multi-scale low-Mach reacting flow processes. In this general context, this work introduces dedicated numerical tools for the resolution of the incompressible Navier-Stokes equations, an important first step when designing an hydrodynamic solver for low-Mach flows. We build a space adaptive numerical scheme to solve incompressible flows in a finite-volume context, that relies on multiresolution analysis with error control. To this end, we introduce a new collocated finite-volume method on adaptive rectangular grids, with an original treatment of the spurious pressure and velocity modes that does not alter the precision of the discretization technique. The adaptive spatial discretization is coupled to a new 3rd-order additive Runge-Kutta method for the incompressible Navier-Stokes equations, combining a 3rd-order, A-stable, stiffly accurate, 4-stage ESDIRK method for the algebraic linear part of these equations, and a 4th-order explicit Runge-Kutta scheme for the nonlinear convective part. We assess the capabilities of this new hydrodynamic solver in terms of speed and efficiency, in the context of scalar transport on adaptive grids.

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salle 623, Séminaire d'analyse numérique

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