3. Numerical method
For the numerical solution of the system (7)-(11) we use the hydrodynamic simulation method developed by Ivanov & Kryukov (1996). This method is based on the numerical scheme which provides high (second or third) order resolution of functions in the regions of their smoothness and preserves their monotonicity at discontinuities. This scheme is a modification of the Godunov scheme and can be attributed either to the TVD (total variation diminishing) or ENO (essentially nonoscillatory) classes depending on the implementation of the code modules. To find the fluxes through the computational cell interfaces, either the exact or some of the approximate solutions to the Riemann problem of the disintegration of an arbitrary discontinuity are used. In order to determine the values of the vector on the right- and left-hand sides of a cell interface, we use a substantially two-dimensional reconstruction procedure. The time integration is performed by the third-order Runge-Kutta method.
© European Southern Observatory (ESO) 2000
Online publication: January 29, 2001