The Community Atmosphere Model (CAM) version 5 includes a spectral element dynamical core option from NCAR’s High-Order Method Modeling Environment. It is a continuous Galerkin spectral finite element method designed for fully unstructured quadrilateral meshes. The current configurations in CAM are based on the cubedsphere grid. The main motivation for including a spectral element dynamical cor...

the liquid metal flow and the solidification behaviours in a multi-cavity casting mould of two automotive cast parts were simulated in three dimensions. the commercial code, flow-3d® was used because it can track the front of the molten metal by a volume of fluid (vof) method and allows complicated parts to be modeled by the fractional area/volume obstacle representation (favor) method. the gre...

in this study prediction of the steady-state flow of branched polymer melts in pipe geometry with finite volume method is presented. our analysis in this study revealed that;for normal-stress tqq , the xpp model can predict this tensor unlike the other viscoelastic models such as ptt or gieskus which can not predict tqq for viscoelastic fluid in two dimensional pipe flows. the fluid is modelled...

Poroelasticity theory models the dynamics of porous, fluid-saturated media. It was pioneered by Maurice Biot in the 1930s through 1960s, and has applications in several fields, including geophysics and modeling of in vivo bone. A wide variety of methods have been used to model poroelasticity, including finite difference, finite element, pseudospectral, and discontinuous Galerkin methods. In thi...

In this paper, we present a discontinuous Galerkin finite clement method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact ste...

We introduce a uniformly convergent iterative method for the systems arising from non-symmetric IIPG linear approximations of second order elliptic problems. The method can be viewed as a block Gauß–Seidel method in which the blocks correspond to restrictions of the IIPG method to suitably constructed subspaces. Numerical tests are included, showing the uniform convergence of the iterative meth...

Modal analysis of the flux reconstruction (FR) formulation is performed to obtain the semi-discrete and fully-discrete dispersion relations, using which, the wave properties of physical as well as spurious modes are characterized. The effect of polynomial order, correction function and solution points on the dispersion, dissipation and relative energies of the modes are investigated. Using this...

We present a new well-balanced finite volume method within the framework of the finite volume evolution Galerkin (FVEG) schemes. The methodology will be illustrated for the shallow water equations with source terms modelling the bottom topography and Coriolis forces. Results can be generalized to more complex systems of balance laws. The FVEG methods couple a finite volume formulation with appr...

For classical discretizations of elliptic partial differential equations, like conforming finite elements or finite differences, block Jacobi methods are equivalent to classical Schwarz methods with minimal overlap, see for example [4]. This is different when the linear system (1) is obtained using DG methods. Our paper is organized as follows: in section 2 we describe several DG methods for li...

We study the iterative solution of dense linear systems that arise from boundary element discretizations of the electrostatic integral equation in magnetoencephalography (MEG). We show that modern iterative methods can be used to decrease the total computation time by avoiding the time-consuming computation of the LU decomposition of the coefficient matrix. More importantly, the modern iterativ...