Solution Remapping Method with Lower Bound Preservation for Navier-Stokes Equations in Aerodynamic Shape Optimization (Communications in Computational Physics, 2023)
It is found that the solution remapping technique proposed in [Numer. Math.Theor. Meth. Appl., 2020, 13(4)] and [J. Sci. Comput., 2021, 87(3): 1-26] does not workout for the Navier-Stokes equations with a high Reynolds number. The shape deformations usually reach several boundary layer mesh sizes for viscous flow, which farexceed one-layer mesh that the original method can tolerate. The direct application toNavier-Stokes equations can result in the unphysical pressures in remapped solutions,even though the conservative variables are within the reasonable range. In this work,a new solution remapping technique with lower bound preservation is proposed toconstruct initial values for the new shapes, and the global minimum density and pressure of the current shape which serve as lower bounds of the corresponding variablesare used to constrain the remapped solutions. The solution distribution provided bythe present method is proven to be acceptable as an initial value for the new shape.Several numerical experiments show that the present technique can substantially accelerate the flow convergence for large deformation problems with 70%-80% CPU timereduction in the viscous airfoil drag minimization.