This paper presents a spectral multidomain method for solving the Navier‐Stokes equations in the vorticity‐stream function formulation. The algorithm is based on an extensive use of the influence matrix technique and so leads to a direct method without any iterative process. Numerical results concerning the Czochralski melt configuration are reported and compared with spectral monodomain solutions to show the advantage of the domain decomposition for such a problem which solution presents a singular behaviour.

A spectral multidomain technique for the computation of the czochralski melt configuration

We numerically simulate a single-mode Rayleigh–Taylor instability between compressible miscible fluids with a highly accurate self-adaptive pseudospectral Chebyshev multidomain method in two two-dimensional boxes at small aspect ratios. The simulations are started from rest and pursued until the return toward mechanical equilibrium of the mixing. Four regimes—linear and weakly nonlinear, nonlinear steady bubble rise, return toward equilibrium, and finally a system of acoustic waves—can be identified. We show that this one-dimensional system of stationary acoustic waves is damped by the physical viscosity. This provides a reference solution.

A return toward equilibrium in a 2D Rayleigh–Taylor instability for compressible fluids with a multidomain adaptive Chebyshev method

A comparison of differential quadrature methods for the solution of partial differential equations

The Chebyshev multidomain technique for calculating solutions with steep gradients is first discussed regarding accuracy and stability in case of simple model equations. Then the method is described for the solution of the Navier-Stokes equations and applications to double-diffusive convection exhibiting thin inner layers are presented.

J. P. Pulicani

Papers

A spectral multi-domain method for the solution of 1-D-Helmholtz and Strokes-type equations