対流項の差分形式とその保存性

抄録

A proper finite difference method based on the gradient/convective form of the equation of motion of incompressible fluid is discussed. The gradient form discretized on the staggered grid has essentially the same conservation properties as those of the divergence/momentum-conservative form or the quadratic-conservative form under some conditions. First, the mass continuity should be numerically satisfied. Second, the numerical consistency between the mass continuity and the momentum convection should be satisfied. The gradient form evaluated at midpoints between velocity points in the direction of convection, rather than directly calculated at velocity points, meets this requirement. In this paper, through mathematical description of the above-mentioned features, the performance of the higher-order finite difference method for the gradient form is demonstrated.