Mesh stretch effects on convection in flow simulations

Staggered grids have been widely used with finite difference approaches for incompressible flow simulation. They retain conservation properties that stabilize the flow field, and avoid odd–even decoupling in the pressure field. On a non-uniform mesh, however, the accuracy of finite difference schemes is degraded to the order of the mesh stretch, if all the conservation properties are to be upheld. This study shows how a non-uniform numerical mesh creates short wavelength errors in convective terms, especially when the grid spacing varies in the streamwise direction. The conservation properties of convective schemes on a non-uniform mesh can conflict with aspects of numerical accuracy. It is crucial to employ an area-weighted average for the convection velocity in order to impose mass conservation in the presence of mesh stretching. Truncation error analysis indicates that energy conserving schemes produce anti-diffusion error if the mesh is stretched, or positive diffusion if it is narrowed. An alternative convection scheme that minimizes the mesh-stretch error is proposed and evaluated through numerical simulations. The nature of mesh stretch error is illustrated by a direct numerical simulation of turbulent channel flow.