A general approach to study and enhance the slope limiter functions on non-uniform grids is presented. Slope limiters are preferred in high-resolutions schemes in general and MUSCL in particular to solve hyperbolic conservation laws. However, most 1D limiters are developed assuming uniform meshes in space, which are shown to be inadequate on non-uniform grids. Especially, secondorder convergenc...

For solving time-dependent convection-dominated partial differential equations (PDEs), which arise frequently in computational physics, high order numerical methods, including finite difference, finite volume, finite element and spectral methods, have been undergoing rapid developments over the past decades. In this article we give a brief survey of two selected classes of high order methods, n...

Superconductor fault current limiter (SFCL) is an effective device to suppress high fault currents. This paper presents a comparative study of resistive and inductive fault current limiters from transient stability point of view.  Appropriate location and type of the limiters in a HV substation is selected by a qualitative approach based on the equal area criterion. Study system is simulated by...

A finite compact (FC) difference scheme requiring only bi-diagonal matrix inversion is proposed by using the known high-resolution flux. Introducing TVD or ENO limiters in the numerical flux, several high-resolution FC-schemes of hyperbolic conservation law are developed, including the FC-TVD, third-order FC-ENO and fifth-order FC-ENO schemes. Boundary conditions formulated need only one unknow...

superconductor fault current limiter (sfcl) is an effective device to suppress high fault currents. this paper presents a comparative study of resistive and inductive fault current limiters from transient stability point of view.  appropriate location and type of the limiters in a hv substation is selected by a qualitative approach based on the equal area criterion. study system is simulated by...

A numerical investigation of high-resolution schemes for solving the compressible Navier-Stokes equations in the context of Implicit Large Eddy Simulation (ILES) is presented. Computations have been performed using a hybrid total variation-diminishing (TVD) scheme. The hybrid TVD scheme combines third-order Godunov-type fluxes with first-order (dissipative) schemes using the flux limiters appro...

It is known that Flux Corrected Transport algorithms can produce entropy-violating solutions of hyperbolic conservation laws. Our purpose to design flux correction with maximal antidiffusive fluxes obtain entropy scalar To do this we consider a hybrid difference scheme linear combination monotone and high-order accuracy. The limiters for the are calculated from corresponding optimization proble...