Magneto-Fluid Dynamics Seminar

High-Order Hybridized Discontinuous Galerkin methods and scalable solvers for Incompressible Resistive Magnetohydrodynamics

Speaker: Sriramkrishnan Muralikrishnan, Paul Scherrer Institut, Switzerland

Location: Warren Weaver Hall 905

Date: Tuesday, February 18, 2020, 11 a.m.


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 bottle neck till 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. For several 2D and 3D transient examples from MHD, including, but not limited to the island coalescence problem at high Lundquist numbers the preconditioner is robust. We also show strong and weak scalability of the block preconditioner up to 8192 cores in the Stampede2 supercomputer.