Оne-dimensional gas dynamics problems and their solution based on high-resolution finite difference schemes

High resolution difference schemes for compressible gas dynamics

High-resolution finite compact difference schemes for hyperbolic conservation laws

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...

High Order Finite Difference Schemes for the Solution of Second Order Initial Value Problems

The numerical solution of second order ordinary differential equations with initial conditions is here approached by approximating each derivative by means of a set of finite difference schemes of high order. The stability properties of the obtained methods are discussed. Some numerical tests, reported to emphasize pros and cons of the approach, motivate possible choices on the use of these for...

Parallel Solution of High Order Finite Difference Schemes for Pricing Multi-dimensional American Options

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Solution of Two-Dimensional Riemann Problems of Gas Dynamics by Positive Schemes

The positivity principle and positive schemes to solve multidimensional hyperbolic systems of conservation laws have been introduced in [X.-D. Liu and P. D. Lax, J. Fluid Dynam., 5 (1996), pp. 133–156. Some numerical experiments presented there show how well the method works. In this paper we use positive schemes to solve Riemann problems for two-dimensional gas dynamics.