A SIMPLE SEMI-LAGRANGIAN SCHEME FOR ADVECTION EQUATIONS

A semi-L-agrangian scheme is proposed by using forward trajectories an d a splitting approach to the interpolation procedure. Several polynom ial interpolation schemes are tested, including cubic spline and Lagra nge polynomials of degree 3, 5 and 7. A simple filter is also proposed to eliminate spurious short waves and to achieve positive-definitenes s. Uniform, rotational and Smolarkiewicz's deformational flows are tes ted, a solution to the inviscid Burger's equation is also provided. Th is new algorithm employing cubic-spline interpolation and the new filt er yields efficient and accurate short-term simulations. The advantage in efficiency of adopting split trajectories for interpolation is acc ompanied by a restriction which is slightly more stringent than the st ability criterion for conventional semi-L-agrangian advection schemes. It is also found that the simple filter can eliminate spurious short waves very effectively without degrading the solutions.