Towards a parameter-free method for high Reynolds number turbulent flow simulation based on adaptive finite element approximation

Abstract

Highlights• We present a parameter-free method for high Reynolds number turbulent flow.• The method is based on adaptive mesh optimization using adjoint techniques.• We connect the numerical approximation to dissipative weak solutions.• Turbulent boundary layers are left unresolved, no boundary layer mesh is needed.• We highlight benchmark problems for which the method is validated. AbstractThis article is a review of our work towards a parameter-free method for simulation of turbulent flow at high Reynolds numbers. In a series of papers we have developed a model for turbulent flow in the form of weak solutions of the Navier-Stokes equations, approximated by an adaptive finite element method, where: (i) viscous dissipation is assumed to be dominated by turbulent dissipation proportional to the residual of the equations, and (ii) skin friction at solid walls is assumed to be negligible compared to inertial effects. The result is a computational model without empirical data, where the only model parameter is the local size of the finite element mesh. Under adaptive refinement of the mesh based on a posteriori error estimation, output quantities of interest in the form of functionals of the finite element solution converge to become independent of the mesh resolution, and thus the resulting method has no adjustable parameters. No ad hoc design of the mesh is needed, instead the mesh is optimized based on solution features, in particular no boundary layer mesh is needed. We connect the computational method to the mathematical concept of a dissipative weak solution of the Euler equations, as a model of high Reynolds number turbulent flow, and we highlight a number of benchmark problems for which the method is validated. The purpose of the article is to present the computational framework in a concise form, to report on recent progress, and to discuss open problems that are subject to ongoing research.

An interface‐tracking unified continuum model for fluid‐structure interaction with topology change and full‐friction contact with application to aortic valves

“…The stabilization of the fluid flow equations in the UC-FSI model ( 27) can be interpreted as a residual based turbulence model, 52 which does not rely on any flow dependent parameters and, therefore, does not need to be reparameterized for different flow regimes. This methodology is well tested in various fields of science, 53 including for the simulation of ventricular blood flow and heart valves. [61][62][63]…”

Mesh Adaptation Using Adjoint Methods and Reduced-Order Models for Large Eddy Simulation

“…However, the speed of data communication between hard disk and solver is much slower than the access to main memory. Others choose to store flow solution snapshots at a prescribed frequency and interpolate intermediate values in time [9,10], which has also been employed in high-Re number problems [11]. Another solution is to apply the checkpointing technique [12] in which optimalselected primal states are stored and then used to re-solve the primal problem locally.…”

Anisotropic boundary layer mesh generation for reliable 3D unsteady RANS simulations

“…The high accuracy requirement for the prediction of integral coecients in aerodynamic simulations often implies the necessity to correctly resolve local ow features such as ow separation, or boundary layers, where the uid velocity exhibits strong gradients in the wall-normal direction, and skin-friction usually plays a dening role [2,3]. It is generally acknowledged that extremely rened meshes are widely required in order to capture global as well as local ow features past simplied and complex geometries, Email address: aurelien.larcher@mines-paristech.fr (A. Larcher) which can often be time and budget consuming.…”