Related papers: Applications of a finite-volume algorithm for inco…
In this paper we analyze a fully discrete scheme for a general Cahn-Hilliard equation coupled with a nonsteady Magneto-hydrodynamics flow, which describes two immiscible, incompressible and electrically conducting fluids with different…
This paper establishes a regularity theory for the magnetohydrodynamics (MHD) equations with external forces through scaling analysis. Inspired by the existing methodology, we utilize linearized approximations and the monotonicity property…
This paper presents a new code for performing multidimensional radiation hydrodynamic (RHD) simulations on parallel computers involving anisotropic radiation fields and nonequilibrium effects. The radiation evolution modules described here…
We develop structure-preserving finite element methods for the incompressible, resistive Hall magnetohydrodynamics (MHD) equations. These equations incorporate the Hall current term in Ohm's law and provide a more appropriate description of…
The aim is to justify rigorously the so-called reduced magnetohydrodynamic model (abbreviated as RMHD), which is widely used in fusion, space and astrophysical plasmas. Motivated by physics, the focus is on plasmas that are simultaneously…
Astrophysical plasmas in relativistic spacetimes, such as black hole accretion flows, are often weakly collisional and require kinetic modeling to capture non-local transport and particle acceleration. However, the extreme scale separation…
In this paper we propose and analyze a mixed DG method and an HDG method for the stationary Magnetohydrodynamics (MHD) equations with two types of boundary (or constraint) conditions. The mixed DG method is based a recent work proposed by…
Coarse grid projection (CGP) is a multiresolution technique for accelerating numerical calculations associated with a set of nonlinear evolutionary equations along with the stiff Poisson equations. In this article we use CGP for the first…
We propose finite-volume schemes for the Cahn-Hilliard equation which unconditionally and discretely preserve the boundedness of the phase field and the dissipation of the free energy. Our numerical framework is applicable to a variety of…
In this work, we design an entropy stable, finite volume approximation for the ideal magnetohydrodynamics (MHD) equations. The method is novel as we design an affordable analytical expression of the numerical interface flux function that…
The theory and application of numerical methods for unstructured meshes have been improved significantly in recent years. Because the grids can be place arbitrarily in space, unstructured meshes can provide much higher spatial resolution…
We present a formalism for importing techniques from dynamical systems theory in the study of three-dimensional magnetohydrodynamic (MHD) equilibria. By treating toroidal angle as time, we reformulate the equilibrium equations as…
We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used…
Whether or not smooth solutions to the 3D compressible magnetohydrodynamic (MHD) equations without magnetic diffusion are always global in time remains an extremely challenging open problem. No global well-posedness or stability result is…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in…
This paper studies the nonlinear evolution of magnetic field turbulence in proximity of steady ideal MHD configurations characterized by a small electric current, a small plasma flow, and approximate flux surfaces, a physical setting that…
A dynamical vectorial equation for homogeneous incompressible Hall-MHD turbulence together with the exact scaling law for third-order correlation tensors, analogous to that for the incompressible MHD, is rederived and applied to the results…
We consider a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are respectively piecewise constant and affine. We use a projection…
Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…