On The Combined Performance Of Non Local Artificial Boundary Conditions With The New Generation Of Advanced Multigrid Flow Solvers

On the Combined Performance of Non-local Artificial Boundary Conditions with the New Generation of Advanced Multigrid Flow Solvers

We develop theoretically and implement numerically a unified flow solution methodology that combines the advantages relevant to two independent groups of methods in CFD that have recently proven successful: The new factorizable schemes for the equations of hydrodynamics that facilitate the construction of optimally convergent multigrid algorithms, and highly accurate global far-field artificial boundary conditions (ABCs). The primary result that we have obtained is the following. Global ABCs do not hamper the optimal (i.e., unimprovable) multigrid convergence rate pertinent to the solver. At the same time, contrary to the standard local ABCs, the solution accuracy provided by the global ABCs deteriorates very slightly or does not deteriorate at all when the computational domain shrinks, which clearly translates into substantial savings of computer resources.

Quadratic Optimization in the Problems of Active Control of Sound

Recent Advances in Achieving Textbook Multigrid Efficiency for Computational Fluid Dynamics Simulations

Recent advances in achieving textbook multigrid efficiency for fluid simulations are presented. Textbook multigrid efficiency is defined as attaining the solution to the governing system of equations in a computational work which is a small multiple of the operation counts associated with discretizing the system. Strategies are reviewed to attain this efficiency by exploiting the factorizability properties inherent to a range of fluid simulations, including the compressible Navier-Stokes equations. factorizability is used to separate the elliptic and hyperbolic factors contributing to the target system; each of the factors can then be treated individually and optimally. Boundary regions and discontinuities are addressed with separate (local) treatments. New formulations and recent calculations demonstrating the attainment of textbook efficiency for aerodynamic simulations are shown.