Related papers: Arbitrary Lagrangian-Eulerian hybridizable discont…
We analyze families of primal high-order hybridizable discontinuous Galerkin (HDG) methods for solving degenerate (second-order) elliptic problems. One major trouble regarding this class of PDEs concerns its mathematical nature, which may…
We propose the application of the arbitrary Lagrangian-Eulerian (ALE) technique to a compressible lattice Boltzmann model for the simulation of moving boundary problems on unstructured meshes. To that end, the kinetic equations are mapped…
We propose a family of high-order local discontinuous Galerkin (LDG) methods, built on a parametric representation and coupled with a semi-implicit backward Euler time discretization, for isotropic and anisotropic curve-shortening flows.…
Our study of the basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics [10,11,12,16] is extended to the case of temperature-dependent surface tension. We prove well-posedness in an Lp-setting,…
We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration…
We present a high-order implicit large eddy simulation (ILES) approach for simulating flows at the nearly incompressible regime. Our methodology based on utilization of a nodal discontinuous Galerkin (DG) discretization of the Boltzmann…
In these lecture notes, we provide an introduction to the theory of mixing for incompressible flows from a PDE perspective. We discuss both the Lagrangian (ODE) and Eulerian (PDE, continuity equation) viewpoints, and introduce suitable…
We discuss general incompressible inviscid models, including the Euler equations, the surface quasi-geostrophic equation, incompressible porous medium equation, and Boussinesq equations. All these models have classical unique solutions, at…
This thesis deals with the investigation of a H(div)-conforming hybrid discontinuous Galerkin discretization for incompressible turbulent flows. The discretization method provides many physical and solving-oriented properties, which may be…
In this paper, we propose a new hybridized discontinuous Galerkin (DG) method for the convection-diffusion problems with mixed boundary conditions. A feature of the proposed method, is that it can greatly reduce the number of…
For the Hodge--Laplace equation in finite element exterior calculus, we introduce several families of discontinuous Galerkin methods in the extended Galerkin framework. For contractible domains, this framework utilizes seven fields and…
We present an enhanced immersed interface method for simulating incompressible fluid flows in thin gaps between closely spaced immersed boundaries. This regime, common in engineered structures such as including tribological interfaces and…
Mixing between two different miscible fluids with a mutual interface must be initiated by fluid transporting across this fluid interface, caused for example by applying an unsteady velocity agitation. In general, there is no necessity for…
In this paper, we propose an enriched Galerkin (EG) approximation for a two-phase pressure saturation system with capillary pressure in heterogeneous porous media. The EG methods are locally conservative, have fewer degrees of freedom…
We propose an discontinuous Galerkin local orthogonal decomposition multiscale method for convection-diffusion problems with rough, heterogeneous, and highly varying coefficients. The properties of the multiscale method and the…
In this article, interior penalty discontinuous Galerkin methods using immersed finite element functions are employed to solve parabolic interface problems. Typical semi-discrete and fully discrete schemes are presented and analyzed.…
A discontinuous Galerkin (dG) method for the numerical solution of initial/boundary value multi-compartment partial differential equation (PDE) models, interconnected with interface conditions, is presented and analysed. The study of…
We begin an investigation of hybridizable discontinuous Galerkin (HDG) methods for approximating the solution of Dirichlet boundary control problems governed by elliptic PDEs. These problems can involve atypical variational formulations,…
In 1966, Arnold [1] showed that the Lagrangian flow of ideal incompressible fluids (described by Euler equations) coincide with the geodesic flow on the manifold of volume preserving diffeomorphisms of the fluid domain. Arnold's proof and…
A discontinuous Galerkin method for the ideal 5 moment two-fluid plasma system is presented. The method uses a second or third order discontinuous Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping scheme. The…