THE THIRD-ORDER ACCURATE POLYNOMIAL METHOD FOR THE CONVECTIVE TERMS APPROXIMATION

摘要

Using the Third-Order upstream Polynomial a new two-dimensional explicit numerical scheme (TOP-12) is developed for accurate approximation of convective terms in the conservation equations. The scheme is utilising 12 nodes, the minimum required to reach the uniform CFL stability condition in two directions. Using smaller and narrower flux stencils compared to other algorithms of similar accuracy, the TOP-12 scheme is more efficient in terms of computations per single node. Numerical tests and comparison with other well-known algorithms show a high performance of the developed scheme. The TOP-12 scheme is applied for investigation of oil slick dynamics on a water surface.