Related papers: The Moving Discontinuous Galerkin Finite Element M…
Grad-div stabilization is a classical remedy in conforming mixed finite element methods for incompressible flow problems, for mitigating velocity errors that are sometimes called poor mass conservation. Such errors arise due to the…
A new hybrid mixed discontinuous Galerkin finite element (HMDGFE) method is constructed for incompressible miscible displacement problem. In this method, the hybrid mixed finite element (HMFE) procedure is considered to solve pressure and…
We present a detailed description and verification of a discontinuous Galerkin finite element method (DG) for the multi-component chemically reacting compressible Navier-Stokes equations that retains the desirable properties of DG, namely…
We present a discontinuous finite element method for the shallow water equations which exploits high-resolution realistic bathymetry data without any regularity assumption, also in the case of high-order discretizations. We prove a number…
Discrete fracture models with reduced-dimensional treatment of conductive and blocking fractures are widely used to simulate fluid flow in fractured porous media. Among these, numerical methods based on interface models are intensively…
This work extends the high-resolution isogeometric analysis approach established for scalar transport equations to the equations of gas dynamics. The group finite element formulation is adopted to obtain an efficient assembly procedure for…
A mixed continuous / discontinuous Galerkin scheme is introduced for the simulation of fluid-structure interaction problems in an isogeometric analysis framework. The properties of Non-Uniform Rational B-Spline basis functions are leveraged…
A discontinuous Galerkin (DG) method suitable for large-scale astrophysical simulations on Cartesian meshes as well as arbitrary static and moving Voronoi meshes is presented. Most major astrophysical fluid dynamics codes use a finite…
A new model for the numerical simulation of a rigid body moving in a viscous fluid flow using FEM is presented. One of the most interesting features of this approach is the small computational effort required to solve the motion of the…
In this work, we propose an accurate, robust, and stable discretization of the gamma-based compressible multicomponent model by Shyue [J. Comput. Phys., 142 (1998), 208-242] where each component follows a stiffened gas equation of state…
An implicit high-order discontinuous Galerkin (DG) method is developed to find steady-state solution of rarefied gas flow described by the Boltzmann equation with full collision operator. In the physical space, velocity distribution…
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.…
We develop a family of cut finite element methods of different orders based on the discontinuous Galerkin framework, for hyperbolic conservation laws with stationary interfaces in both one and two space dimensions, and for moving interfaces…
Purpose: This study aims to assess the accuracy of degree adaptive strategies in the context of incompressible Navier-Stokes flows using the high order hybridisable discontinuous Galerkin (HDG) method. Design/methodology/approach: The work…
Sliding meshes are a powerful method to treat deformed domains in computational fluid dynamics, where different parts of the domain are in relative motion. In this paper, we present an efficient implementation of a sliding mesh method into…
A family of weak Galerkin finite element discretization is developed for solving the coupled Darcy-Stokes equation. The equation in consideration admits the Beaver-Joseph-Saffman condition on the interface. By using the weak Galerkin…
We present a discontinuous Galerkin method for moist atmospheric dynamics, with and without warm rain. By considering a combined density for water vapour and cloud water, we avoid the need to model and compute a source term for…
This paper is concerned with developing accurate and efficient numerical methods for one-dimensional fully nonlinear second order elliptic and parabolic partial differential equations (PDEs). In the paper we present a general framework for…
We consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the…
We propose an unfitted interface penalty Discontinuous Galerkin-Finite Element Method (UIPDG-FEM) for elliptic interface problems. This hybrid method combines the interior penalty discontinuous Galerkin (IPDG) terms near the…