Accession Number:

ADA606728

Title:

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

Descriptive Note:

Technical rept.

Corporate Author:

NATIONAL INST OF AEROSPACE ASSOCIATES HAMPTON VA

Report Date:

2014-03-01

Pagination or Media Count:

37.0

Abstract:

A time-dependent extension of the first-order hyperbolic system method J. Comput. Phys., 227 2007315-352 for advection-diffusion problems is introduced. Diffusiveviscous terms are written and discretized as a hyperbolic system, which recovers the original equation in the steady state. The resulting scheme orders advantages over traditional schemes a dramatic simplification in the discretization, high-order accuracy in the solution gradients, and orders-of-magnitude convergence acceleration. The hyperbolic advection-diffusion system is discretized by the second-order upwind residual-distribution scheme in a unified manner, and the system of implicit-residual-equations is solved by Newtons method over every physical time step. The numerical results are presented for linear and nonlinear advection-diffusion problems, demonstrating solutions and gradients produced to the same order of accuracy, with rapid convergence over each physical time step, typically less than five Newton iterations.

Subject Categories:

  • Operations Research
  • Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE