An implementation of the Spalart–Allmaras DES model in an implicit unstructured hybrid finite volume/element solver for incompressible turbulent flow

Abstract

SUMMARYIn this paper, we describe an implicit hybrid finite volume (FV)/element (FE) incompressible NavierStokes solver for turbulent flows based on the Spalart-Allmaras detached eddy simulation (SA-DES). The hybrid FV/FE solver is based on the segregated pressure correction or projection method. The intermediate velocity field is first obtained by solving the original momentum equations with the matrix-free implicit cell-centered FV method. The pressure Poisson equation is solved by the node-based Galerkin FE method for an auxiliary variable. The auxiliary variable is closely related to the real pressure and is used to update the velocity field and the pressure field. We store the velocity components at cell centers and the auxiliary variable at vertices, making the current solver a staggered-mesh scheme. The SA-DES turbulence equation is solved after the velocity and the pressure fields have been updated at the end of each time step. The same matrix-free FV method as the one used for momentum equations is used to solve the turbulence equation. The turbulence equation provides the eddy viscosity, which is added to the molecular viscosity when solving the momentum equation. In our implementation, we focus on the accuracy, efficiency and robustness of the SA-DES model in a hybrid flow solver. This paper will address important implementation issues for high-Reynolds number flows where highly stretched elements are typically used. In addition, some aspects of implementing the SA-DES model will be described to ensure the robustness of the turbulence model. Several numerical examples including a turbulent flow past a flat plate and a high-Reynolds number flow around a high angle-of-attack NACA0015 airfoil will be presented to demonstrate the accuracy and efficiency of our current implementation.

CaMEL and ADCIRC Storm Surge Models—A Comparative Study

“…The finite volume (FV) method is used to discretize this system in space and solve for the velocity field using the Newton-Raphson iterative method [18,19]. After the computational domain is discretized into conforming elements, the finite volume formulation can be written for each control volume.…”

“…In this context u n+1 is an intermediate velocity field during the nonlinear iteration and the balance between u and u n+1 will be enforced through the gradient of h . This process is similar to the projection methods commonly used to solve incompressible Navier Stokes equations [18][19][20]. Note that as h → 0 , then ∇h → 0 which ensures u n+1 → u .…”

“…areas ( [18,19], to name a few). It has moving mesh capabilities to solve problems with highly nonlinear structural deformations.…”

A hybrid scheme based on finite element/volume methods for two immiscible fluid flows

“…This deployment provides a convenient way to evaluate the pressure gradient using the local FE basis functions without the need of reconstruction as required for the velocity field. Refer to [1,8] for more details.…”

An Improved Scale-Adaptive Simulation Model for Massively Separated Flows

“…It is well known that the DES concept combines the advantages of RANS and LES methods in a simple and effective way by using the grid spacing as an adjusting scale, which has been proven promising for engineering flows, and a variety of hybrid approaches have since appeared [3,7]. However, the DES models are not without problems [8,9], and the main stumbling stone for DES is the ambiguous response to the grid refinement. When exceeding a critical level of grid refinement near walls, the standard DES formulation may negatively impact the RANS performance and arise some issues, such as, gray area, modeled stress depletion (MSD), and grid-induced separation (GIS) [10].…”