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DY: Fachverband Dynamik und Statistische Physik
DY 32: Poster: Active Matter, Soft Matter, Fluids
DY 32.26: Poster
Mittwoch, 20. März 2024, 15:00–18:00, Poster C
High-order finite volume numerics to achieve low numerical diffusivity — •Jean-Mathieu Teissier1, Raquel Mäusle1, and Wolf-Christian Müller1,2 — 1Technische Universität, Berlin, Germany — 2Max-Planck/Princeton Center for Plasma Physics
Natural systems typically present turbulent dynamics at Reynolds numbers not yet achievable with current computing facilities. The discretization of the governing equations leads to a loss of energy over time, which can be partially modelled by a so-called “numerical viscosity”, which gives an upper bound to the achievable Reynolds number for a given solver at a given numerical grid-size. Hence, finding ways to (i) minimize this loss of energy and (ii) quantify the dissipation of numerical nature is crucial to perform more realistic simulations. We present high-order dimension-by-dimension finite-volume solvers for the Navier-Stokes and magnetohydrodynamics equations, with discretization orders up to ten. Although higher-order schemes are more costly at a given grid-size, they allow results of similar quality on significantly coarser grids as compared to, e.g. second-order schemes. This leads to an overall gain in computing efficiency, typically a factor of order 10–100. In order to quantify the improvement of the numerical viscosity and magnetic diffusivity of the solvers with discretization order, we present simulations of the tearing mode instability, whose growth rate is a function of (physical) viscosity and magnetic diffusivity.
Keywords: High-order numerics; Finite-volume; Magnetohydrodynamics; Tearing mode instability; Numerical dissipation