Divergence-free velocity fields in nonperiodic geometries
Journal of Computational Physics
A spectral method for polar coordinates
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
An efficient spectral-projection method for the Navier--Stokes equations in cylindrical geometries
Journal of Computational Physics
The integral equation method for a steady kinematic dynamo problem
Journal of Computational Physics
Journal of Computational Physics
An interior penalty Galerkin method for the MHD equations in heterogeneous domains
Journal of Computational Physics
Spectral method for matching exterior and interior elliptic problems
Journal of Computational Physics
Poloidal-toroidal decomposition in a finite cylinder
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
The Navier-Stokes equations and magnetohydrodynamics equations are written in terms of poloidal and toroidal potentials in a finite cylinder. This formulation insures that the velocity and magnetic fields are divergence-free by construction, but leads to systems of partial differential equations of higher order, whose boundary conditions are coupled. The influence matrix technique is used to transform these systems into decoupled parabolic and elliptic problems. The magnetic field in the induction equation is matched to that in an exterior vacuum by means of the Dirichlet-to-Neumann mapping, thus eliminating the need to discretize the exterior. The influence matrix is scaled in order to attain an acceptable condition number.