We study some of the properties of a line-based discontinuous Galerkin (DG) scheme for the compressible Euler and Navier-Stokes equations. The scheme is based on fully unstructured meshes of quadrilateral or hexahedral elements, and it is closely related to the standard nodal DG scheme as well as several of its variants such as the collocation-based DG spectral element method (DGSEM) or the spe...

the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the ri...

• Two novel strongly hyperbolic reformulations of a model for surface tension. Godunov-Powell-type formulation PDE with curl-type involutions. Generalized Lagrangian multiplier (GLM) approach Long-time simulations stationary and oscillating bubbles shock-bubble interaction. High order ADER discontinuous Galerkin schemes posteriori subcell finite volume limiter. In this work, we introduce two th...

This paper deals with the construction of high-order ADER numerical schemes for solving the one-dimensional shallow water equations with variable bed elevation. The non-linear version of the schemes is based on ENO reconstructions. The governing equations are expressed in terms of total water height, instead of total water depth, and discharge. The ENO polynomial interpolation procedure is also...

For numerical schemes to the incompressible Navier-Stokes equations with variable density, it is a critical property preserve bounds of density. A bound-preserving high order accurate scheme can be constructed by using discontinuous Galerkin (DG) methods or finite volume limiter for density evolution equation, any popular method momentum evolution. In this paper, we consider combination continu...

In this paper, we propose a new conservative hybrid finite element-finite difference method for the Vlasov equation. The proposed methodology uses Strang splitting to decouple the nonlinear high dimensional Vlasov equation into two lower dimensional equations, which describe spatial advection and velocity acceleration/deceleration processes respectively. We then propose to use a semi-Lagrangian...

The Gi-coupled adenine receptor (AdeR) binds adenine with high affinity and potentially reduces cellular cAMP levels. Since cAMP is an important second messenger in the renal transport of water and solutes, we localized AdeR in the rat kidney. Real-time RT-PCR showed higher relative expression of AdeR mRNA in the cortex and outer medulla compared with the inner medulla. Immunoblots using a pept...

For the integration of distributed generation (DG) units to the utility grid, voltage source converter (VSC) is the key technology. In order to realize high quality power injection, different control techniques have been adopted. However, the converter-based DG interface is subject to inevitable uncertainties, which adversely influence the performance of the controller. The interfacing impedanc...

The discontinuous Galerkin (DG) method has been popular as a numerical technique for solving the conservation laws of gas dynamics. In the present study, we develop an explicit modal DG scheme for multi-dimensional conservation laws on unstructured triangular meshes in conjunction with non-Newtonian implicit nonlinear coupled constitutive relations (NCCR). Special attention is given to how to t...

We propose a space-time finite volume scheme on moving Chimera grids for general advection-diffusion problem. Special care is devoted to grid overlapping zones in order devise compact and accurate discretization stencil exchange information between different mesh patches. Like the arbitrary high derivatives method, equations are discretized slab. Thus, instead of time-dependent spatial transmis...