The pseudo-spectral method is proposed for following the evolution of density and velocity uctuations at the weakly non-linear stage in the expanding universe with a good accuracy. In this method, the evolution of density and velocity uctuations is integrated in the Fourier Space with using FFT. This method is very useful to investigate accurately the non-linear dynamics in the weakly non-linea...

We present and test a new hybrid numerical method for simulating layerwise-twodimensional geophysical flows. The method radically extends the original ContourAdvective Semi-Lagrangian (CASL) algorithm (Dritschel & Ambaum, 1997) by combining three computational elements for the advection of general tracers (e.g. potential vorticity, water vapor, etc.): (1) a pseudo-spectral method for large scal...

We apply polynomial approximation methods—known in the numerical PDEs context as spectral methods—to approximate the vector-valued function that satisfies a linear system of equations where the matrix and the right-hand side depend on a parameter. We derive both an interpolatory pseudospectral method and a residual-minimizing Galerkin method, and we show how each can be interpreted as solving a...

Fluid motion driven by planetary libration may play a key role in maintaining the magnetism of synchronous planets and moons that are thermally or chemically non-convective. We present a fully discrete finite element method on a triaxial ellipsoidal domain for simulating a three-dimensional nonlinear flow in a latitudinally librating triaxial ellipsoidal cavity, for which the usual pseudo-spect...

This paper analyzes the stability and convergence of the Fourier pseudospectral method coupled with a variety of specially designed time-stepping methods of up to fourth order, for the numerical solution of a three dimensional viscous Burgers’ equation. There are three main features to this work. The first is a lemma which provides for an L2 and H 1 bound on a nonlinear term of polynomial type,...

We present a simple iterative scheme to solve numerically a regularized internal wave model describing the large amplitude motion of the interface between two layers of different densities. Compared with the original strongly nonlinear internal wave model of Miyata [10] and Choi and Camassa [2], the regularized model adopted here suppresses shear instability associated with a velocity jump acro...

The present work proposes a collocation spectral method for solving the three-dimensional Navier-Stokes equations using cylindrical coordinates. The whole diameter −R ≤ r ≤ R is discretized with an even number of radial Gauss-Lobatto collocation points and an angular shift is introduced in the Fourier transform that avoid pole and parity conditions usually required. The method keeps the spectra...

In this paper, we perform a careful numerical study of nearly singular solutions of the 3D incompressible Euler equations with smooth initial data. We consider the interaction of two perturbed antiparallel vortex tubes which was previously investigated by Kerr in [14, 17]. In our numerical study, we use both the pseudo-spectral method with the 2/3 dealiasing rule and the pseudo-spectral method ...