A high-order mass-lumping procedure for B-spline collocation method with application to incompressible flow simulations

This paper presents new developments of the staggered spline collocation method for cost-effective solution to the incompressible Navier-Stokes equations. Maximal decoupling of the velocity and the pressure is obtained by using the fractional step method of Gresho and Chan, allowing the solution to sparse elliptic problems only. In order to preserve the high-accuracy of the B-spline method, this fractional step scheme is used in association with a sparse approximation to the inverse of the consistent mass matrix. Such an approximation is constructed from local spline interpolation method, and represents a high-order generalization of the mass-lumping technique of the finite-element method. A numerical investigation of the accuracy and the computational efficiency of the resulting semi-consistent spline collocation schemes is presented. These schemes generate a stable and accurate unsteady Navier-Stokes solver, as assessed by benchmark computations.