7 citations · 18 across the 21 of their papers we have counts for
22 papers
A second-order structure- and positivity-preserving convex limiting method for the Vlasov equations
Katharina Kormann, Murtazo Nazarov, Junjie Wen
In this paper, we introduce a novel second-order, positivity-preserving finite element method for the Vlasov equations using a convex limiting algorithm. The method employs strong-…
High-Order Structure-Preserving SBP Finite Difference Methods for the Vlasov-Maxwell System on Matrix-Free GPUs
Robin Dymér, Ken Mattsson, Murtazo Nazarov
In this paper, we present a high-order, stable summation-by-parts (SBP) finite difference method for solving the Vlasov-Maxwell system in a 2D2V phase space. Central SBP operators…
A structure-preserving Numerical Method for the Compressible Resistive-Hall-MHD System
Murtazo Nazarov, Rafael Rodriguez-Velasco, Ignacio Tomas
In this paper, we present a structure-preserving method for the compressible resistive Hall-magnetohydrodynamics (MHD) model. The differential operator is split into two parts: a h…
Positivity-preserving dynamical low-rank methods for the Vlasov equation
Katharina Kormann, Murtazo Nazarov, Junjie Wen
In this manuscript, we introduce positivity-preserving correction methods for low-rank approximations of the Vlasov equation. The key idea is to formulate structural properties, in…
High-Order Invariant-Domain Preserving Continuous Finite Elements via Graph-Poisson Convex Limiting
Murtazo Nazarov
We develop a high-order invariant-domain preserving continuous finite element method for nonlinear scalar conservation laws. The method combines a residual-viscosity high-order dis…
A structure-preserving finite element framework for the Vlasov-Maxwell system
Katharina Kormann, Murtazo Nazarov, Junjie Wen
We present a stabilized, structure-preserving finite element framework for solving the Vlasov-Maxwell equations. The method uses a tensor product of continuous polynomial spaces fo…
Revisiting the Slip Boundary Condition: Surface Roughness as a Hidden Tuning Parameter
Matthias Maier, Peter Munch, Murtazo Nazarov
In this paper, we investigate the effect of boundary surface roughness on numerical simulations of incompressible fluid flow past a cylinder in two and three spatial dimensions fur…
An anisotropic nonlinear stabilization for finite element approximation of Vlasov-Poisson equations
Junjie Wen, Murtazo Nazarov
We introduce a high-order finite element method for approximating the Vlasov-Poisson equations. This approach employs continuous Lagrange polynomials in space and explicit Runge-Ku…
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…
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…
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…
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…
A finite element based Heterogeneous Multiscale Method for the Landau-Lifshitz equation
Lena Leitenmaier, Murtazo Nazarov
We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, a simple model for a ferromagnetic composite. A finit…
Stability estimates for radial basis function methods applied to linear scalar conservation laws
Igor Tominec, Murtazo Nazarov, Elisabeth Larsson
We derive stability estimates for three commonly used radial basis function (RBF) methods to solve hyperbolic time-dependent PDEs: the RBF generated finite difference (RBF-FD) meth…
Residual viscosity stabilized RBF-FD methods for solving nonlinear conservation laws
Igor Tominec, Murtazo Nazarov
In this paper, we solve nonlinear conservation laws using the radial basis function generated finite difference (RBF-FD) method. Nonlinear conservation laws have solutions that ent…
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…
Regularity of almost periodic solutions of Poisson's equation
Érgash Muhamadiev, Murtazo Nazarov
This paper discusses some regularity of almost periodic solutions of the Poisson's equation in , where is an almost periodic function. It has been prove…
Numerical Simulations of Surface-Quasi Geostrophic Flows on Periodic Domains
Andrea Bonito, Murtazo Nazarov
We propose a novel algorithm for the approximation of surface-quasi geostrophic (SQG) flows modeled by a nonlinear partial differential equation coupling transport and fractional d…
Second-order invariant domain preserving approximation of the Euler equations using convex limiting
Jean-Luc Guermond, Murtazo Nazarov, Bojan Popov +1
A new second-order method for approximating the compressible Euler equations is introduced. The method preserves all the known invariant domains of the Euler system: positivity of…