Many of the recently developed high-resolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block of these schemes is the averaging of an approximate Godunov solver; its time consuming part involves the field-by-field decomposition which is required in order to identify the “direction of the wind.” Instead, we propose to use as a building block the mor...

In this paper, the Lax-Wendroff difference scheme has been presented for solving one-dimensional wave equation with integral boundary conditions. First, given solution domain is discretized and derivative involving spatial variable replaced by central finite approximation of functional values at each grid point using Taylor series expansion. Then, resulting second-order linear ordinary differen...

We present a (partial) historical summary of the mathematical analysis finite difference and volume methods, paying special attention to Lax–Richtmyer Lax–Wendroff theorems. then state consistency result for convection operators on staggered grids (often used in fluid flow simulations), which illustrates recent generalization flux notion designed cope with general discrete functions.

We investigate oneand multi-dimensional stability of noncharacteristic boundary layers in the limit approaching a standing planar shock wave Ū(x1), x1 > 0, obtaining necessary conditions of (i) weak stability of the limiting shock, (ii) weak stability of the constant layer u ≡ U− := limz→−∞ Ū(z), and (iii) nonnegativity of a modified Lopatinski determinant similar to that of the inviscid shock ...

Abstract We discuss a high order accurate numerical boundary condition for solving hyperbolic conservation laws on fixed Cartesian grids, while the physical domain can be arbitrarily shaped and moving. Compared with body-fitted meshes, the biggest advantage of Cartesian grids is that the grid generation is trivial. The challenge is however that the physical boundary does not usually coincide wi...

An efficient finite difference model of blood flow through the coronary vessels is developed and applied to a geometric model of the largest six generations of the coronary arterial network. By constraining the form of the velocity profile across the vessel radius, the three-dimensional Navier–Stokes equations are reduced to one-dimensional equations governing conservation of mass and momentum....

This paper presents a chemical species transport model to account for variable composition and gas properties along the flow path in internal combustion engines. It is described the numerical solution to adapt the gas dynamic model to chemical species transport in boundary conditions by means of the Method of Characteristics and in volumes by means of a filling and emptying model. The performan...

Abstract. In this paper, we give a survey and discuss new developments and computational results for a high order accurate numerical boundary condition based on finite difference methods for solving hyperbolic equations on Cartesian grids, while the physical domain can be arbitrarily shaped. The challenges are the wide stencil for the high order scheme and the fact that the physical boundary do...