Barriers to Achieving Textbook Multigrid Efficiency (TME) in CFD

Achi Brandt_Abstract"Textbook multigrid efficiency" (TME) means solving a discrete PDE prob-lem in a computational work which is only a small (less than 10) multiple of theoperation count in the discretized system of equations itself. As a guide to attain-ing this optimal performance for general CFD problems, the table below lists everyforeseen kind of computational difficulty for achieving that goal, together with thepossible ways for resolving that difficulty, their current state of development, andreferences.Included in the table are staggered and nonstaggered, conservative and non-conservative discretizations of viscous and inviscid, incompressible and compress-ible flows at various Mach numbers, as well as a simple (algebraic) turbulencemodel and comments on chemically reacting flows. The listing of associated com-putational barriers involves: non-alignment of streamlines or sonic characteristicswith the grids; recirculating flows; stagnation points; discretization and relax-ation on and near shocks and boundaries; far-field artificial boundary conditions;smMl-scale singularities (meaning important features, such as the complete air-plane, which are not visible on some of the coarse grids); large grid aspect ratios;boundary layer resolution; and grid adaption.Introduction (by James L. Thomas, NASA LaRC)Computational fluid dynamics (CFD) is becoming a more important part ofthe complete aircraft design cycle because of the availability of faster computerswith more memory and improved numerical algorithms. As an example, all of theexternal cruise-surface shapes of the new Boeing 777 wide-body subsonic transportwere designed with CFD [R1]. The cruise shape of such a vehicle is designed tominimize viscous and shock wave losses at transonic speeds and can be analyzedwith potential flow methods coupled with interacting boundary layers. Off-designperformance associated with maximum lift, buffet, and flutter and the determina-tion of stability and control derivatives, involving unsteady separated and vortical

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