A semi-Lagrangian method for turbulence simulations using mixed spectral discretizations
The paper describes a spectral semi-Lagrangian method for solving three-dimensional incompressible Navier-Stokes equations. A turbulent channel flow is considered with two homogeneous directions where periodic boundary conditions are imposed, and with one inhomogeneous direction where no-slip conditions are applied. The corresponding space discretization uses Fourier collocation in two homogeneous directions and a spectral element technique with Jacobi polynomials in the inhomogeneous direction. The time-discretization is second-order accurate for both Navier-Stokes equations in Lagrangian form and for the characteristic equations. For the latter an explicit backward integration is used, and the interpolation of velocity at departure points is performed by direct summation of Fourier expansions, which is computationally expensive. The spectral convergence of the method in space and the non-monotonic behaviour of temporal error are studied for an exact solution of three-dimensional Navier-Stokes equations. Finally, direct numerical simulations of a turbulent channel flow are presented, and the results of semi-Lagrangian method are compared with those obtained by an Eulerian scheme.
three-dimensional incompressible Navier-Stokes equations
scientific article; zbMATH DE number 1784264