finite and boundary element methods have been used by many authors to solve mathematicalphysics problems. however, the coupling of these two methods happens to be more efficient as it combinestheir merits. in this paper, the mathematical analysis of the coupling of finite and boundary element methodsfor the helmholtz equation is presented.

This thesis deals with the numerical solution of the Boltzmann transport equation using an expansion of the distribution function in spherical harmonics for the purpose of electronic device simulation. Both the mathematical and physical backgrounds are discussed, then the Boltzmann transport equation is projected onto spherical harmonics without posing unnecessary restrictions on the energy ban...

We describe a hybrid method based on the combined use of the Fourier Galerkin and finite-volume techniques to solve the fluid dynamics equations in cylindrical geometries. A Fourier expansion is used in the angular direction, partially translating the problem to the Fourier space and then solving the resulting equations using a finite-volume technique. We also describe an algorithm required to ...

The aim of this paper is to present a new well-balanced finite volume scheme for two-dimensional multilayer shallow water flows including wet/dry fronts. The ideas, presented here for the two-layer model, can be generalized to a multilayer case in a straightforward way. The method developed here is constructed in the framework of the Finite Volume Evolution Galerkin (FVEG) schemes. The FVEG met...

The aim of this paper is to compare some recent numerical schemes for solving hyperbolic conservation laws. We consider the flux vector splitting finite volume methods, finite volume evolution Galerkin scheme as well as the discontinuous Galerkin scheme. All schemes are constructed using time explicit discretization. We present results of numerical experiments for the shallow water equations fo...

Heat transfer phenomena of flat plate solar collector filled with different nanofluids has been investigated numerically. Galerkin’s Finite Element Method is used to solve the problem. Heat transfer rate, average bulk temperature, average sub-domain velocity, outlet temperature, thermal efficiency, mean entropy generation and Bejan number has been investigated by varying the solid nanoparticle ...

The subject of the paper is the derivation and analysis of third order nite volume evolution Galerkin schemes for the two-dimensional wave equation system. To achieve this the rst order approximate evolution operator is considered. A recovery stage is carried out at each level to generate a piecewise polynomial approximation ~ U n = RhU n 2 S h from the piecewise constantU 2 S h , to feed into ...

In this paper, we present a positivity-preserving high order finite volume Hermite weighted essentially non-oscillatory (HWENO) scheme for compressible Euler equations based on the framework for constructing uniformly high order accurate positivity-preserving discontinuous Galerkin and finite volume schemes for Euler equations proposed in [20]. The major advantages of the HWENO schemes is their...