Wall modeling via function enrichment within a high‐order DG method for RANS simulations of incompressible flow. (16th August 2017)

• Record Type: Journal Article
• Authors: Krank, Benjamin; Kronbichler, Martin; Wall, Wolfgang A.
• Is Part Of: International journal for numerical methods in fluids. Volume 86:Number 1(2018)
• Page Start: 107
• Page End: 129
• Publication Date: 2017-08-16
• Subjects: high‐order discontinuous Galerkin -- RANS -- Spalart‐Allmaras -- wall modeling -- XFEM -- wall functions; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4409
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: We present a novel approach to wall modeling for the Reynolds‐averaged Navier‐Stokes equations within the discontinuous Galerkin method. Wall functions are not used to prescribe boundary conditions as usual, but they are built into the function space of the numerical method as a local enrichment, in addition to the standard polynomial component. The Galerkin method then automatically finds the optimal solution among all shape functions available. This idea is fully consistent and gives the wall model vast flexibility in separated boundary layers or high adverse pressure gradients. The wall model is implemented in a high‐order discontinuous Galerkin solver for incompressible flow complemented by the Spalart‐Allmaras closure model. As benchmark examples, we present turbulent channel flow starting from R e τ =180 and up to R e τ =100000 as well as flow past periodic hills at Reynolds numbers based on the hill height of R e H =10595 and R e H =19000. Abstract : We present a novel approach to wall modeling for the Reynolds‐averaged Navier‐Stokes equations within the discontinuous Galerkin method. The velocity profile in a turbulent boundary layer is composed of the standard polynomial component plus an enrichment component, which is constructed using Spalding's law‐of‐the‐wall. This composition results in a much higher degree of flexibility in strong nonequilibrium boundary layers and mesh independence than common wall functions can provide.