An adaptive multi-moment FVM approach for incompressible flows

In this study, a multi-moment finite volume method (FVM) based on block-structured adaptive Cartesian mesh is proposed for simulating incompressible flows. A conservative interpolation scheme following the idea of the constrained interpolation profile (CIP) method is proposed for the prolongation operation of the newly created mesh. A sharp immersed boundary (IB) method is used to model the immersed rigid body. A moving least squares (MLS) interpolation approach is applied for reconstruction of the velocity field around the solid surface. An efficient method for discretization of Laplacian operators on adaptive meshes is proposed. Numerical simulations on several test cases are carried out for validation of the proposed method. For the case of viscous flow past an impulsively started cylinder (Re=3000,9500), the computed surface vorticity coincides with the result of the body-fitted method. For the case of a fast pitching NACA 0015 airfoil at moderate Reynolds numbers (Re=10000,45000), the predicted drag coefficient (CD) and lift coefficient (CL) agree well with other numerical or experimental results. For 2D and 3D simulations of viscous flow past a pitching plate with prescribed motions (Re=5000,40000), the predicted CD, CL and CM (moment coefficient) are in good agreement with those obtained by other numerical methods.