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math.NA2024
Viscous regularization of the MHD equations
Tuan Anh Dao, Lukas Lundgren, Murtazo Nazarov
Nonlinear conservation laws such as the system of ideal magnetohydrodynamics (MHD) equations may develop singularities over time. In these situations, viscous regularization is a c…
math.NA2023
A fully conservative and shift-invariant formulation for Galerkin discretizations of incompressible variable density flow
Lukas Lundgren, Murtazo Nazarov
This paper introduces a formulation of the variable density incompressible Navier-Stokes equations by modifying the nonlinear terms in a consistent way. For Galerkin discretization…
math.NA2022
A high-order artificial compressibility method based on Taylor series time-stepping for variable density flow
Lukas Lundgren, Murtazo Nazarov
In this paper, we introduce a fourth-order accurate finite element method for incompressible variable density flow. The method is implicit in time and constructed with the Taylor s…