Fast and Scalable solvers for High-Order Finite Element Methods with applications to Fluid Dynamics and Magnetohydrodynamics

by Sriramkrishnan Muralikrishnan (PSI - Paul Scherrer Institut)

Thursday 28 Nov 2019, 14:00 → 15:00 Europe/Zurich

OFLG/401 (Paul Scherrer Institut)

High-order methods are useful for simulating hyperbolic conservation laws commonly arising in many applications of fluid dynamics, electromagnetics and magnetohydrodynamics. They not only provide greater accuracy per computational cost when compared to lower order methods, but also a necessity to obtain correct dispersion properties. We consider here a particular high-order finite element method namely, hybridized discontinuous Galerkin method (HDG) suitable for current and future computing architectures. One of the attractive features of HDG methods is that they have lot fewer coupled unknowns at high orders in the context of steady state problems or time dependent problems with implicit time stepping. However, for practically large-scale simulations the linear system arising from HDG methods still present a bottleneck until date.
In this talk, we present a block preconditioning strategy for incompressible visco-resistive magnetohydrodynamics (MHD) equations discretized with high-order HDG methods. MHD equations play an important role in modeling low Lundquist number liquid metal flows, high Lundquist number large-guide-field fusion plasmas and low flow-Mach-number compressible flows. They present several challenges in terms of nonlinearity, coupled fluid and magnetic physics, incompressibility constraints in both velocity and magnetic fields to name a few. With several 2D and 3D transient examples, we demonstrate the robustness and parallel scalability of the block preconditioner.