Numerical Benchmark Solutions for Laminar and Turbulent Flows

Numerical benchmark solutions are numerical solutions that have been computed using a verified code and with a high degree of rigorously assessed numerical accuracy. They can bridge the gap between simple problems where the analytic solution to the differential equations is known and more complex problems where exact solutions are not known. In particular, benchmark numerical solutions can be used for code verification (i.e., algorithm and code correctness), assessing discretization error estimators, and evaluating solution adaptation strategies. The requirements for establishing a numerical benchmark solution are discussed. A numerical benchmark is created for a turbulent flat plate using the Spalart-Allmaras Reynolds-Averaged Navier-Stokes (RANS) turbulence model. Three computational fluid dynamics codes are employed to provide additional confidence in the final benchmark solution: Loci-CHEM, FUN3D, and CFL3D. A numerical benchmark is also created for a supersonic manufactured solution and Ringleb’s flow, both with known exact solutions, to ensure that the recommended guidelines for generating a numerical benchmark solution are sufficient.

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