Search results for "Runge–Kutta method"
showing 4 items of 14 documents
A computational magnetohydrodynamic model of a marine propulsion system
2016
In this article we present an approach to the description of Magnetohydrodynamic Propulsion. Preliminarly, an analytical model which includes an electromagnetic model and a thermal model is presented. Successively, in order to move beyond the analytical model, a 3-D MHD modeling tool and a Runge Kutta method based solver are presented and they are used to investigate an alternative MHD solutions. Some numerical analysis are given.
Partially Implicit Runge-Kutta Methods for Wave-Like Equations
2014
Runge-Kutta methods are used to integrate in time systems of differential equations. Implicit methods are designed to overcome numerical instabilities appearing during the evolution of a system of equations. We will present partially implicit Runge-Kutta methods for a particular structure of equations, generalization of a wave equation; the partially implicit term refers to this structure, where the implicit term appears only in a subset of the system of equations. These methods do not require any inversion of operators and the computational costs are similar to those of explicit Runge-Kutta methods. Partially implicit Runge-Kutta methods are derived up to third-order of convergence. We ana…
Equilibrium real gas computations using Marquina's scheme
2003
Marquina's approximate Riemann solver for the compressible Euler equations for gas dynamics is generalized to an arbitrary equilibrium equation of state. Applications of this solver to some test problems in one and two space dimensions show the desired accuracy and robustness
Generalized singly-implicit Runge-Kutta methods with arbitrary knots
1985
The aim of this paper is to derive Butcher's generalization of singly-implicit methods without restrictions on the knots. Our analysis yields explicit computable expressions for the similarity transformations involved which allow the efficient implementation of the first phase of the method, i.e. the solution of the nonlinear equations. Furthermore, simple formulas for the second phase of the method, i.e. computation of the approximations at the next nodal point, are established. Finally, the matrix which governs the stability of the method is studied.