The idea of a microgrid is created by utilizing more diverse ac or dc distributed generation (DG) sources along with an energy storage system (ESS) and loads. The most efficient and reliable selection of ac and dc microgrids is a hybrid ac/dc microgrid. The hybrid microgrid largely overcomes the shortcomings of standalone ac or dc microgrids. A bidirectional interlinking converter (BIC) is util...

Put options are commonly used in the stock market to protect against the decline of the price of a stock below a specified price. On the other hand, finite difference approach is a well-known and well-resulted numerical scheme for financial differential equations. As such in this work, a new spatial discretization based on finite difference semi-discretization procedure with high order of accur...

We compare different block preconditioners in the context of parallel time adaptive higher order implicit time integration using Jacobian-free Newton-Krylov (JFNK) solvers for discontinuous Galerkin (DG) discretizations of the three dimensional time dependent Navier-Stokes equations. A special emphasis of this work is the performance for a relative high number of processors, i.e. with a low num...

In this paper, we discuss the formulation, stability and validation of a high-order non-dissipative discontinuous Galerkin (DG) method for solving Maxwell’s equations on non-conforming simplex meshes. The proposed method combines a centered approximation for the numerical fluxes at inter element boundaries, with either a second-order or a fourth-order leap-frog time integration scheme. Moreover...

In this paper, we develop a family of high order asymptotic preserving schemes for some discrete-velocity kinetic equations under a diffusive scaling, that in the asymptotic limit lead to macroscopic models such as the heat equation, the porous media equation, the advectiondiffusion equation, and the viscous Burgers’ equation. Our approach is based on the micromacro reformulation of the kinetic...

In this paper, we present a conservative cell-centered Lagrangian Finite Volume scheme for solving the hyperelasticity equations on unstructured multidimensional grids. The starting point of approach is FV discretization named EUCCLHYD and introduced in context hydrodynamics. Here, it combined with posteriori Multidimensional Optimal Order Detection (MOOD) limiting strategy to ensure robustness...

We propose a family of high order methods for solution of hyperbolic conservation laws which are based on the discontinuous Galerkin (DG) spatial discretization. In the standard DG method, the dispersion and dissipation errors and the spectrum of the semi-discrete scheme are related to the [ p p+1 ] Padé approximants of exp(z) and exp(−z). These Padé approximants are responsible for the superco...