Results for “multi-stage preconditioning”

NASA NTRS1999

Efficient Multi-Stage Time Marching for Viscous Flows via Local Preconditioning

A new method has been developed to accelerate the convergence of explicit time-marching, laminar, Navier-Stokes codes through the combination of local preconditioning and multi-stage time marching optimization. Local preconditioning is a technique to modify the time-dependent equations so that all information moves or decays at nearly the same rate, thus relieving the stiffness for a system of equations. Multi-stage time marching can be optimized by modifying its coefficients to account for the presence of viscous terms, allowing larger time steps. We show it is possible to optimize the time marching scheme for a wide range of cell Reynolds numbers for the scalar advection-diffusion equation, and local preconditioning allows this optimization to be applied to the Navier-Stokes equations. Convergence acceleration of the new method is demonstrated through numerical experiments with circular advection and laminar boundary-layer flow over a flat plate.

Kleb, William L.↗

NASA NTRS1999

Efficient Multi-Stage Time Marching for Viscous Flows via Local Preconditioning

A new method has been developed to accelerate the convergence of explicit time-marching, laminar, Navier-Stokes codes through the combination of local preconditioning and multi-stage time marching optimization. Local preconditioning is a technique to modify the time-dependent equations so that all information moves or decays at nearly the same rate, thus relieving the stiffness for a system of equations. Multi-stage time marching can be optimized by modifying its coefficients to account for the presence of viscous terms, allowing larger time steps. We show it is possible to optimize the time marching scheme for a wide range of cell Reynolds numbers for the scalar advection-diffusion equation, and local preconditioning allows this optimization to be applied to the Navier-Stokes equations. Convergence acceleration of the new method is demonstrated through numerical experiments with circular advection and laminar boundary-layer flow over a flat plate.

Kleb, William L.↗

NASA NTRS1993

Computation of propulsion-related flowfields using unstructured adaptive meshes

In this paper, we describe a computational fluid dynamics (CFD) technique based on unstructured triangular/tetrahedral meshes. A finite-volume scheme is used in conjunction with a multi-stage Runge-Kutta algorithm. Convergence enhancements in the form of dual time-stepping and time-derivative preconditioning are used to overcome the limitations of conventional multi-stage schemes. The method is applied to propulsion-related flows and shown to perform satisfactorily.

Weiss, Jonathan M.↗

NASA NTRS1989

Design of optimally smoothing multi-stage schemes for the Euler equations

In this paper, a method is developed for designing multi-stage schemes that give optimal damping of high-frequencies for a given spatial-differencing operator. The objective of the method is to design schemes that combine well with multi-grid acceleration. The schemes are tested on a nonlinear scalar equation, and compared to Runge-Kutta schemes with the maximum stable time-step. The optimally smoothing schemes perform better than the Runge-Kutta schemes, even on a single grid. The analysis is extended to the Euler equations in one space-dimension by use of 'characteristic time-stepping', which preconditions the equations, removing stiffness due to variations among characteristic speeds. Convergence rates independent of the number of cells in the finest grid are achieved for transonic flow with and without a shock. Characteristic time-stepping is shown to be preferable to local time-stepping, although use of the optimally damping schemes appears to enhance the performance of local time-stepping. The extension of the analysis to the two-dimensional Euler equations is hampered by the lack of a model for characteristic time-stepping in two dimensions. Some results for local time-stepping are presented.

Van Leer, Bram↗