First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems
NATIONAL INST OF AEROSPACE ASSOCIATES HAMPTON VA
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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.
- Operations Research
- Fluid Mechanics