Abstract
This paper presents the finite-surface method for solving the Navier-Stokes equations (NSE). This method defines the velocities as a surface-averaged value on the surfaces of the pressure cells. Consequently, the mass conservation on the pressure cells becomes an exact equation. The only things left to approximate is the momentum equation and the pressure at the new time step. At certain conditions, the exact mass conservation enables the explicit n-th order accurate NSE solver to be used with the pressure treatment that is two or four order less accurate without losing the apparent convergence rate. This feature was not possible with finite volume of finite difference methods. The convergence rate for laminar flows are presented. In addition to these result which was already presented elsewhere, this work presents a resolution criteria needed to achieve a DNS-like solution. The turbulent channel flow with friction Reynolds number 590 is used in this study. Previously, it was found that a fourth-order scheme is effectively 10X faster than the second-order scheme, at the comparable accuracy. The newly developed sixth-order FSM is 4X faster than the fourth-order scheme and thus it is a very interesting numerical method for solving turbulent flow. This speedup is possible due to the reduction of the number of grid points.
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