Related papers: A discontinuous Galerkin method for a diffuse-inte…
In this paper, a high order quasi-conservative discontinuous Galerkin (DG) method using the non-oscillatory kinetic flux is proposed for the 5-equation model of compressible multi-component flows with Mie-Gr\"uneisen equation of state. The…
In this paper, we present an efficient numerical algorithm for solving the time-dependent Cahn--Hilliard--Navier--Stokes equations that model the flow of two phases with different densities. The pressure-correction step in the projection…
In this article, using the weighted discrete least-squares, we propose a patch reconstruction finite element space with only one degree of freedom per element. As the approximation space, it is applied to the discontinuous Galerkin methods…
In this article, we propose a novel conservative diffuse-interface method for the simulation of immiscible compressible two-phase flows. The proposed method discretely conserves the mass of each phase, momentum and total energy of the…
One of the challenges when simulating astrophysical flows with self-gravity is to compute the gravitational forces. In contrast to the hyperbolic hydrodynamic equations, the gravity field is described by an elliptic Poisson equation. We…
In this work we develop a methodology to approximate the covariance matrix associated to the simulation of water diffusion inside the brain tissue. The computation is based on an implementation of the Discontinuous Galerkin method of the…
Relativistic plasmas around compact objects can sometimes be approximated as being force-free. In this limit, the plasma inertia is negligible and the overall dynamics is governed by global electric currents. We present a novel numerical…
In this paper, we describe a numerical technique for the solution of macroscopic traffic flow models on networks of roads. On individual roads, we consider the standard Lighthill-Whitham-Richards model which is discretized using the…
In this paper we consider a conservative discretization of the two-dimensional incompressible Navier--Stokes equations. We propose an extension of Arakawa's classical finite difference scheme for fluid flow in the vorticity-stream function…
The flow of incompressible fluids through porous media plays a crucial role in many technological applications such as enhanced oil recovery and geological carbon-dioxide sequestration. The flow within numerous natural and synthetic porous…
We assess the ability of three different approaches based on high-order discontinuous Galerkin methods to simulate under-resolved turbulent flows. The capabilities of the mass conserving mixed stress method as structure resolving large eddy…
In this work we introduce the development of a three--phase incompressible Navier--Stokes/Cahn--Hilliard numerical method to simulate three--phase flows, present in many industrial operations. The numerical method is then applied to…
This paper proposes a diffuse-interface model for simulating gas-liquid-solid multiphase flows involving solid-liquid phase change, solute transport, and the Marangoni effect. In this model, a phase-field method is employed to capture the…
In this work, we use a moving Voronoi and sharp interface approach for simulating two-phase flows. At every time step, the mesh is generated anew from Voronoi seeds that behave as material points. The paper is a continuation of our previous…
In this paper, we study a model for the transport of an external component, e.g., a surfactant, in variably saturated porous media. We discretize the model in time and space by combining a backward Euler method with the linear Galerkin…
A convergence result for a discontinuous Galerkin multiscale method for a second order elliptic problem is presented. We consider a heterogeneous and highly varying diffusion coefficient in $L^\infty(\Omega,\mathbb{R}^{d\times d}_{sym})$…
We consider a system of second order non-linear elliptic partial differential equations that models the equilibrium configurations of a two dimensional planar bistable nematic liquid crystal device. Discontinuous Galerkin finite element…
We formulate hydrodynamic equations and spectrally accurate numerical methods for investigating the role of geometry in flows within two-dimensional fluid interfaces. To achieve numerical approximations having high precision and level of…
The mass flow rate of Poiseuille flow of rarefied gas through long ducts of two-dimensional cross-sections with arbitrary shape are critical in the pore-network modeling of gas transport in porous media. In this paper, for the first time,…
We present a hybrid continuous and discontinuous Galerkin spectral element approximation that leverages the advantages of each approach. The continuous Galerkin approximation is used on interior element faces where the equation properties…