16 citations · 79 across the 44 of their papers we have counts for
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A nodal based high order nonlinear stabilization for finite element approximation of Magnetohydrodynamics
Tuan Anh Dao, Murtazo Nazarov
We present a novel high-order nodal artificial viscosity approach designed for solving Magnetohydrodynamics (MHD) equations. Unlike conventional methods, our approach eliminates th…
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…
Structure preserving numerical methods for the ideal compressible MHD system
Tuan Anh Dao, Murtazo Nazarov, Ignacio Tomas
We introduce a novel structure-preserving method in order to approximate the compressible ideal Magnetohydrodynamics (MHD) equations. This technique addresses the MHD equations usi…
Monolithic parabolic regularization of the MHD equations and entropy principles
Tuan Anh Dao, Murtazo Nazarov
We show at the PDE level that the monolithic parabolic regularization of the equations of ideal magnetohydrodynamics (MHD) is compatible with all the generalized entropies, fulfill…
A high-order residual-based viscosity finite element method for the ideal MHD equations
Tuan Anh Dao, Murtazo Nazarov
We present a high order, robust, and stable shock-capturing technique for finite element approximations of ideal MHD. The method uses continuous Lagrange polynomials in space and e…
Energy stable and accurate coupling of finite element methods and finite difference methods
Tuan Anh Dao, Ken Mattsson, Murtazo Nazarov
We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order finite difference methods in a nonconforming multiblock fashion. The aim is to opti…