Related papers: A direction preserving discretization for computin…
A diffused-interface approach based on the Allen-Cahn phase field equation is developed within a high-order Discontinuous Galerkin framework. The interface capturing technique is based on the balance between explicit diffusion and…
In this study, we consider the simulation of subsurface flow and solute transport processes in the stationary limit. In the convection-dominant case, the numerical solution of the transport problem may exhibit non-physical diffusion and…
Transport properties of degenerate relativistic electrons along quantizing magnetic fields in neutron star crusts are considered. A kinetic equation is derived for the spin polarization density matrix of electrons. Its solution does not…
In this work we use algebraic dual representations in conjunction with domain decomposition methods for Darcy equations. We define the broken Sobolev spaces and their finite dimensional counterparts. In addition, a global trace space is…
We present a novel numerical framework for studying nonlinear dispersive equations in higher-dimensional settings, specifically designed for solutions featuring traveling waves along a preferred axis (or field-aligned traveling waves).…
We develop an explicit second order staggered finite difference discretization scheme for simulating the transport of highly heterogeneous gas mixtures through pipeline networks. This study is motivated by the proposed blending of hydrogen…
This paper is concerned with structure-preserving numerical approximations for a class of nonlinear nonlocal Fokker-Planck equations, which admit a gradient flow structure and find application in diverse contexts. The solutions,…
The radiative transfer equation models the interaction of radiation with scattering and absorbing media and has important applications in various fields in science and engineering. It is an integro-differential equation involving time,…
We consider the non-isothermal flow of a compressible fluid through pipes. Starting from the full set of Euler equations, we propose a variational characterization of solutions that encodes the conservation of mass, energy, and entropy in a…
In this paper we formulate and test numerically a fully-coupled discontinuous Galerkin (DG) method for incompressible two-phase flow with discontinuous capillary pressure. The spatial discretization uses the symmetric interior penalty DG…
We present a new temporal discretization paradigm for developing energy-production-rate preserving numerical approximations to thermodynamically consistent partial differential equation systems, called the supplementary variable method. The…
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…
We present a scalable 2D Galerkin spectral element method solution to the linearized potential flow radiation problem for wave induced forcing of a floating offshore structure. The pseudo-impulsive formulation of the problem is solved in…
In this paper, we consider control constrained $L^2-$Dirichlet boundary control of a convection-diffusion equation on a two dimensional convex polygonal domain. We discretize the control problem based on the local discontinuous Galerkin…
Surface sensitive electric current measurements are important experimental tools poorly corroborated by theoretical models. We show that the drift-diffusion equations offer a framework for a consistent description of such experiments. The…
One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent…
The effects of the propagation of particles which have a finite life-time and an according broad distribution in their mass spectrum are discussed in the context of a transport descriptions. In the first part some example cases of mesonic…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
We present a convergent and constraint-preserving numerical discretization of a mathematical model for the dynamics of a liquid crystal subjected to an electric field. This model can be derived from the Oseen-Frank director field theory,…
The Fokker-Planck equation can be reformulated as a continuity equation, which naturally suggests using the associated velocity field in particle flow methods. While the resulting probability flow ODE offers appealing properties - such as…