Mixed Jacobi-spherical harmonic spectral method for Navier--Stokes equations

Authors:
Ben-Yu Guo;Wei Huang
Affiliations:
Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China Division of Computational Science of E-institute of Shanghai Universities;Department of Mathematics, Shanghai University, Shanghai, 200436, China
Venue:
Applied Numerical Mathematics
Year:
2007

Citing 7
Cited 3

Combined finite element and pseudospectral method for the two-dimensional evolutionary Navier-Stokes equations

SIAM Journal on Numerical Analysis
A spectral method for the vorticity equation on the surface

Mathematics of Computation
A spectral method for the fluid flow with low Mach number on the spherical surface

SIAM Journal on Numerical Analysis
Efficient Spectral-Galerkin Methods IV. Spherical Geometries

SIAM Journal on Scientific Computing
Gegenbauer Approximation in Certain Hilbert Spaces and Its Applications to Singular Differential Equations

SIAM Journal on Numerical Analysis
Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces

Journal of Approximation Theory
A standard test set for numerical approximations to the shallow water equations in spherical geometry

Journal of Computational Physics

Navier-Stokes spectral solver in a sphere

Journal of Computational Physics
An optimal Galerkin scheme to solve the kinematic dynamo eigenvalue problem in a full sphere

Journal of Computational Physics
Stability and Convergence Analysis of Fully Discrete Fourier Collocation Spectral Method for 3-D Viscous Burgers' Equation

Journal of Scientific Computing

Quantified Score

Hi-index	0.01

Visualization

Abstract

Mixed Jacobi-spherical harmonic spectral method is proposed for the Navier-Stokes equations in a ball. Its stability and convergence are proved. Numerical results demonstrate the efficiency of this approach. Some results on the mixed Jacobi-spherical harmonic approximation are established, which play important role in numerical analysis of spectral method in spherical geometry.