In [18], two of the authors developed a high order accurate numerical boundary condition procedure for hyperbolic conservation laws on a Cartesian mesh, which allows the computation using high order finite difference schemes on Cartesian meshes to solve problems in arbitrary physical domains whose boundaries do not coincide with grid lines. This procedure is based on the so-called inverse Lax-W...

Computer simulation of the thermodynamics and dynamics of an intercooled two-stage two-cylinder reciprocating air compressor system is reported and the obtained results discussed. The main emphasis is placed upon modeling the pressure-wave motion in the interconnecting pipework for which the governing equations were solved by means of two different methods: the characteristic mesh method and th...

Abstract — An upwind and a Lax-Wendroff scheme are introduced for the solution of a one dimensional non-local problem modelling Ohmic heating of Foods. The schemes are studied regarding their consistency, stability and the rate of convergence for the cases that the problem attains a global solution in time. A high resolution scheme is also introduced and it is shown that it is total-variation-s...

A mathematical model is developed of a spring-loaded pressure relief valve connected to a reservoir of compressible fluid via a single, straight pipe. The valve is modelled using Newtonian mechanics, under assumptions that the reservoir pressure is sufficient to ensure choked flow conditions. The usual assumptions of ideal gas theory lead to a system of first-order partial differential equation...

We develop a high order numerical boundary condition for compressible inviscid flows involving complex moving geometries. It is based on finite difference methods on fixed Cartesian meshes which pose a challenge that the moving boundaries intersect the grid lines in an arbitrary fashion. Our method is an extension of the so-called inverse Lax-Wendroff procedure proposed in [16] for conservation...

In this paper, we present an intensive investigation of the finite volume method (FVM) compared to difference methods (FDMs). order show main in way approaching solution, take Burgers equation and Buckley–Leverett as examples simulate previously mentioned methods. On one hand, results using schemes Lax–Friedrichs Lax–Wendroff. other apply Godunov’s scheme method. Moreover, how starting with a v...

The article discusses substantiating the parameters brake system of a tractor-trailer (TT). section offers comparative analysis theoretical and experimental studies TT drive its elements. Based on that, ordinary differential equations were solved by Runge - Kutta method, first-order accuracy (Euler's method). To solve partial equations, we used modified Lax Wendroff scheme. results obtained usi...