Engineering topics

Wimmer, Golo Albert

Publications and source records attributed to Wimmer, Golo Albert.

3 records

DOE OSTI2024

Structure preserving transport stabilized compatible finite element methods for magnetohydrodynamics

Here, we present compatible finite element space discretizations for the ideal compressible magnetohydrodynamic equations. The magnetic field is considered both in div- and curl-conforming spaces, leading to a strongly or weakly preserved zero-divergence condition, respectively. The equations are discretized in space such that transfers between the kinetic, internal, and magnetic energies are consistent, leading to a preserved total energy. We also discuss further adjustments to the discretization required to additionally achieve magnetic helicity preservation. Finally, we describe new transport stabilization methods for the magnetic field equation which maintain the zero-divergence and energy conservation properties, including one method which also preserves magnetic helicity. The methods' preservation and improved stability properties are confirmed numerically using a steady state and a magnetic dynamo test case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Superior discretizations and AMG solvers for extremely anisotropic diffusion via hyperbolic operators [Slides]

Diffusion in magnetic confinement fusion is extremely anisotropic in the direction of field lines. Rewrote diffusion system based on directional gradients, apply discretization and solver techniques developed for advection. Orders of magnitude decrease in error and solve wallclock time vs. traditional methods. The next steps include: (1) incorporate into larger MHD simulations, (2) better solvers for closed field lines or mixed regimes, and (3) possibly other extremely anisotropic equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Improving the accuracy of discretisations of the vector transport equation on the lowest-order quadrilateral Raviart-Thomas finite elements

Within finite element models of fluids, vector-valued fields such as velocity or momentum variables are commonly discretised using the Raviart-Thomas elements. However, when using the lowest-order quadrilateral Raviart-Thomas elements, standard finite element discretisations of the vector transport equation typically have a low order of spatial accuracy. This paper describes two schemes that improve the accuracy of transporting such vector-valued fields on two-dimensional curved manifolds. The first scheme that is presented reconstructs the transported field in a higher-order function space, where the transport equation is then solved. The second scheme applies a mixed finite element formulation to the vector transport equation, simultaneously solving for the transported field and its vorticity. In this work, an approach to stabilising this mixed vector-vorticity formulation is presented that uses a Streamline Upwind Petrov-Galerkin (SUPG) method. These schemes are then demonstrated, along with their accuracy properties, through some numerical tests. Two new test cases are used to assess the transport of vector-valued fields on curved manifolds, solving the vector transport equation in isolation. The improvement of the schemes is also shown through two standard test cases for rotating shallow-water models.

97 MATHEMATICS AND COMPUTING↗