Conservative properties of finite difference schemes for incompressible flow (3rd report, numerical tests)

Abstract

In this report, numerical tests of the conservation properties of finite difference schemes are performed. Inviscid flow simulations in a two-dimensional periodic domain are performed using several finite difference schemes that are discussed in the first and second reports. The momentum and kinetic energy are conserved when the proper schemes in regular and staggered grid systems are used. The defect of the finite difference schemes in a collocated grid system is emphasized in the simulation. In addition, plane channel flows at Re=180 and 2 000 are simulated using the proper fourth-order accurate finite difference scheme in a staggered grid system and the results are better than those of the second-order accurate algorithm and an existing fourth-order accurate scheme.