Murtazo Nazarov
Division of Scientific Computing, IT Department, Uppsala University
In this talk, we present an invariant-domain-preserving finite element approximation of nonlinear conservation laws. In particular, a surface-quasi-geostrophic equation (SQG). The SQG equation is a scalar equation derived from the system of incompressible Euler equations that models geophysical processes for fluids with s strong rotation, and is widely used in atmospheric simulations. Despite the fact that this is a scalar equation, there are two main difficulties in numerically approximating this equation: 1. the equation includes a fractional Laplace operator, which is a non-local operator; 2. the numerical method must preserve the invariant domain or the maximum principle. We present our approach to addressing these two issues.
The talk is based on our recently published article:
Numerical Simulations of Surface Quasi-Geostrophic Flows on Periodic Domains. A Bonito, M Nazarov - SIAM Journal on Scientific Computing, 2021 https://epubs.siam.org/doi/abs/10.1137/20M1342616