The challenge of electricity distribution’s upgrade to incorporate new technologies is big, and electric utilities are mandated to work diligently on this agenda, thus making investments to ensure that current networks maintain their electricity supply commitments secure and reliable in face of disruptions and adverse environmental conditions from a variety of sources. The paper presents a new ...

In this paper we investigate a nonlinear evolution model described by the Rosenau-KdV equation. We propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of O(τ2 + h2). Furthermore we show the existence and uniqueness of numerical solutions. Comparing the numerical results with other methods in...

Efficient solution techniques for high-order accurate time-dependent problems are investigated for solving the two-dimensional non-linear Euler equations in this work. The spatial discretization consists of a high-order accurate Discontinuous Galerkin (DG) approach. Implicit time-integration techniques are considered exclusively in order to avoid the stability restrictions of explicit methods. ...

In this paper, a high order quasi-conservative discontinuous Galerkin (DG) method using the non-oscillatory kinetic flux is proposed for 5-equation model of compressible multi-component flows with Mie-Gr\"uneisen equation state. The mainly consists three steps: firstly, DG used to solve conservative equations model; secondly, inspired by Abgrall's idea, we derive scheme volume fraction which ca...

In this work a robust discontinuous Galerkin (DG) solver for turbulent high-lift aerodynamic flows using the turbulence model of Spalart and Allmaras (SA) is developed. The application of DG discretizations to turbulent RANS flows is one of the most pressing issues facing high-order methods on unstructured grids. The issue is the result of non-smooth behavior of the turbulence model equation, w...

Achieving higher accuracy and fidelity in aerodynamic simulations using higher-order methods has received significant attention over the last decade. High-order methods are attractive because they provide higher accuracy with fewer degrees of freedom and at the same time relieve the burden of generating very fine meshes. Discontinuous Galerkin (DG) methods1 have received particular attention fo...

Numerical simulations are becoming increasingly important in the design of micromechanical resonators, in particular for the prediction of complex frequency response in high quality devices. This is particularly true when there is need to accurately predict damping due to anchor losses and other complex wave interactions. Frequency based approaches have been shown to predict these accurately, h...

The finite volume (FV) method is the dominating discretization technique for computational fluid dynamics (CFD), particularly in the case of compressible fluids. The discontinuous Galerkin (DG) method has emerged as a promising highaccuracy alternative. The standardDGmethod reduces to a cell-centered FVmethod at lowest order. However, many of today’s CFD codes use a vertex-centered FV method in...