We present novel numerical schemes for the incompressible Navier-Stokes equations with
variable density and address two critical concerns, ie, the preservation of lower density …

We present a novel asymptotic-preserving semi-implicit finite element method for weakly
compressible and incompressible flows based on compatible finite element spaces. The …

We construct a structure-preserving finite element method and time-stepping scheme for
inhomogeneous, incompressible magnetohydrodynamics (MHD). The method preserves …

We present a finite element variational integrator for compressible flows. The numerical
scheme is derived by discretizing, in a structure-preserving way, the Lie group formulation of …

We construct finite element methods for the incompressible magnetohydrodynamics (MHD)
system that precisely preserve the magnetic and cross helicity, the energy law and the …

Respecting the laws of thermodynamics is crucial for ensuring that numerical simulations of
dynamical systems deliver physically relevant results. In this paper, we construct a structure …

The motion of ions in the complex fluids widely appears in biofluids, hydrodynamics,
geodynamics and geophysics. Performing efficient and accurate computation for …

This paper introduces a formulation of the variable density incompressible Navier-Stokes
equations by modifying the nonlinear terms in a consistent way. For Galerkin discretizations …

Simulating transient and compressible multi-fluid flows in extreme situations such as Inertial
Confinement Fusion is especially challenging because of numerous and sometimes …

We propose a new class of finite element approximations to ideal compressible
magnetohydrodynamic equations in smooth regime. Following variational approaches …