Boundary conditions for incompressible flows
Journal of Scientific Computing
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Mixed laguerre-legendre pseudospectral method for incompressible fluid flow in an infinite strip
Mathematics of Computation
Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
Journal of Approximation Theory
Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials
Journal of Scientific Computing
Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation)
Generalized Jacobi polynomials/functions and their applications
Applied Numerical Mathematics
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In this paper, we propose a spectral method for the $$n$$ n -dimensional Navier---Stokes equations with slip boundary conditions by using divergence-free base functions. The numerical solutions fulfill the incompressibility and the physical boundary conditions automatically. Therefore, we need neither the artificial compressibility method nor the projection method. Moreover, we only have to evaluate the unknown coefficients of expansions of $$n-1$$ n 驴 1 components of the velocity. These facts simplify actual computation and numerical analysis essentially, and also save computational time. As the mathematical foundation of this new approach, we establish some approximation results, with which we prove the spectral accuracy in space of the proposed algorithm. Numerical results demonstrate its high efficiency and coincide the analysis very well. The main idea, the approximation results and the techniques developed in this paper are also applicable to numerical simulations of other problems with divergence-free solutions, such as certain partial differential equations describing electro-magnetic fields.