Poloidal-toroidal decomposition in a finite cylinder. I: Influence matrices for the magnetohydrodynamic equations

DOI10.1016/j.jcp.2007.08.023zbMath1126.76055arXiv0705.0608OpenAlexW2065043512MaRDI QIDQ2465008

Piotr Boronski, Laurette S. Tuckerman

Publication date: 18 December 2007

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.0608

zbMATH Keywords

compatibility conditionsDirichlet-to-Neumann mappingmatrix conditioning

Mathematics Subject Classification ID

Spectral methods applied to problems in fluid mechanics (76M22) Magnetohydrodynamics and electrohydrodynamics (76W05)

Related Items

Micro-object motion tracking based on the probability hypothesis density particle tracker ⋮ A spectral method for the wave equation of divergence-free vectors and symmetric tensors inside a sphere ⋮ Dynamic stabilisation of Rayleigh–Plateau modes on a liquid cylinder ⋮ An efficient spectral code for incompressible flows in cylindrical geometries ⋮ Computing with Functions in the Ball ⋮ Poloidal-toroidal decomposition in a finite cylinder. II: Discretization, regularization and validation ⋮ Spectral methods for numerical relativity ⋮ Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan-Shepp ridge polynomials, Chebyshev-Fourier series, cylindrical Robert functions, Bessel-Fourier expansions, square-to-disk conformal mapping and radial basis functions

Cites Work

• Unnamed Item
• An integro-differential formulation for magnetic induction in bounded domains: Boundary element--finite volume method
• The integral equation method for a steady kinematic dynamo problem
• An efficient spectral-projection method for the Navier-Stokes equations in cylindrical geometries. II: Three-dimensional cases
• An interior penalty Galerkin method for the MHD equations in heterogeneous domains
• Spectral method for matching exterior and interior elliptic problems
• Divergence-free velocity fields in nonperiodic geometries
• The effect of nonzero \(\bigtriangledown\cdot B\) on the numerical solution of the magnetohydrodynamic equations
• Stability and transition in shear flows
• The \(\nabla \cdot B=0\) constraint in shock-capturing magnetohydrodynamics codes
• A spectral method for polar coordinates
• Thermal convection in vertical cylinders. A method based on potentials of velocity
• Poloidal-toroidal decomposition in a finite cylinder. II: Discretization, regularization and validation
• On magnetic boundary conditions for non-spectral dynamo simulations
• On boundary conditions for velocity potentials in confined flows: Application to Couette flow
• A spectral solver for the Navier–Stokes equations in the velocity–vorticity formulation
• Magnetohydrodynamics measurements in the von Kármán sodium experiment
• Effects of truncation in modal representations of thermal convection
• The 1[ratio2 mode interaction in exactly counter-rotating von Kármán swirling flow]
• Hydromagnetic Taylor–Couette flow: numerical formulation and comparison with experiment
• Simulation of Taylor-Couette flow. Part 2. Numerical results for wavy-vortex flow with one travelling wave
• Non-linear spirals in the Taylor–Couette problem