Numerical solution of Boussinesq equations as a model of interfacial-wave propagation.
Numerical studies of vertically propagating acoustic and magneto-acoustic waves in an isothermal atmosphere.
Numerical study of a descending sphere in a low Reynolds number strongly stratified fluid.
Numerical study of free interface problems using boundary integral methods.
Numerical study of the Davey-Stewartson system
We deal with numerical analysis and simulations of the Davey-Stewartson equations which model, for example, the evolution of water surface waves. This time dependent PDE system is particularly interesting as a generalization of the 1-d integrable NLS to 2 space dimensions. We use a time splitting spectral method where we give a convergence analysis for the semi-discrete version of the scheme. Numerical results are presented for various blow-up phenomena of the equation, including blowup of defocusing,...
Numerical study of the Davey-Stewartson system
We deal with numerical analysis and simulations of the Davey-Stewartson equations which model, for example, the evolution of water surface waves. This time dependent PDE system is particularly interesting as a generalization of the 1-d integrable NLS to 2 space dimensions. We use a time splitting spectral method where we give a convergence analysis for the semi-discrete version of the scheme. Numerical results are presented for various blow-up phenomena of the equation, including blowup of defocusing,...