20,701 research outputs found
A semi-implicit Hall-MHD solver using whistler wave preconditioning
The dispersive character of the Hall-MHD solutions, in particular the
whistler waves, is a strong restriction to numerical treatments of this system.
Numerical stability demands a time step dependence of the form for explicit calculations. A new semi--implicit scheme for
integrating the induction equation is proposed and applied to a reconnection
problem. It it based on a fix point iteration with a physically motivated
preconditioning. Due to its convergence properties, short wavelengths converge
faster than long ones, thus it can be used as a smoother in a nonlinear
multigrid method
A moving mesh method for one-dimensional hyperbolic conservation laws
We develop an adaptive method for solving one-dimensional systems of hyperbolic conservation laws that employs a high resolution Godunov-type scheme for the physical equations, in conjunction with a moving mesh PDE governing the motion of the spatial grid points. Many other moving mesh methods developed to solve hyperbolic problems use a fully implicit discretization for the coupled solution-mesh equations, and so suffer from a significant degree of numerical stiffness. We employ a semi-implicit approach that couples the moving mesh equation to an efficient, explicit solver for the physical PDE, with the resulting scheme behaving in practice as a two-step predictor-corrector method. In comparison with computations on a fixed, uniform mesh, our method exhibits more accurate resolution of discontinuities for a similar level of computational work
Adaptive time-stepping for incompressible flow. Part II: Navier-Stokes equations
We outline a new class of robust and efficient methods for solving the Navier- Stokes equations. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams-Bashforth method for error control, and a robust Krylov subspace solver for the spatially discretized system. We present numerical experiments illustrating the potential of our approach. © 2010 Society for Industrial and Applied Mathematics
- …