The discontinuous Galerkin (DG) or local discontinuous Galerkin (LDG) method is a spatial discretization procedure for convection-diffusion equations, which employs useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters. The LaxWendroff time discretization procedure is an alternative method for time d...

In this paper, we review the development of the Runge–Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge–Kutta time discretizations, that allows the m...

sedimentation is one of the most important problems in harbors that results in considerable economic costs. harbor planforms affects the flow pattern in the harbor basin and consequently, plays an important role in sediment transport and sedimentation. in the present study, a two dimensional depth-averaged hydrodynamic and sediment transport model has been developed to investigate the effect of...

this paper introduces a mesh generating algorithm for solving the traffic flow equation as a conservation law equation. the idea behind the new method is to use the characteristic curves and moving non-oscillatory finite volume method. in addition, when characteristic curves intersect, the proposed scheme uses shock speed equation in order to improve computational efficiency. we also compare...

The 2-D 3-T heat conduction equations can be used to approximately describe the energy broadcast in materials and the energy swapping between electron and photon or ion. To solve the equations, a fully implicit finite volume scheme is often used as the discretization method. Because the energy diffusion and swapping coefficients have a strongly nonlinear dependence on the temperature, and some ...

Abstract. We design and analyze a new non-conforming domain decomposition method based on Schwarz type approaches that allows for the use of Robin interface conditions on non-conforming grids. The method is proven to be well posed, and the iterative solver to converge. The error analysis is performed in 2D piecewise polynomials of low and high order and extended in 3D for P1 elements. Numerical...

A boundary layer analysis is presented for the mixed convection past a vertical plate in a porous medium saturated with a nanofluid in the presence of variable viscosity effect. The governing partial differential equations are transformed into a set of similar equations and solved numerically by an efficient, implicit, iterative, finite-difference method. A parametric study illustrating the inf...

Moving-mesh unstructured Finite Volume Method (FVM) is a good candidate for tackling flow simulations where the shape of the domain changes during the simulation or represents a part of the solution. For efficient and user-friendly approach to the problem, it is necessary to automatically determine the point positions in the mesh, based on the prescribed boundary motion. In this paper, we prese...

Multigrid schemes for high order finite difference methods on summationby-parts form are studied by comparing the effect of different interpolation operators. By using the standard linear prolongation and restriction operators, the Galerkin condition leads to inaccurate coarse grid discretizations. In this paper, an alternative class of interpolation operators that bypass this issue and preserv...