Second Order Accuracy N-S Equations for Incompressible Flow

Abstract

Classical N-S equation is of first order accuracy in both time and space. First order scheme only includes first order terms, without the terms of second or higher order. These terms are relative to time and space intervals. As basic elements of fluid research, time and space intervals should be some finite quantities and not be infinitely near to zero as defined in mathematics. If the terms of second or higher order can be ignored depends on the value of related derivative multiplied. Compared with first order terms, the terms of second or higher order can be ignored under the condition of laminar flow. However, under the condition of turbulent flow, these canpsilat be ignored. When turbulent flow develops fully, first order terms, compared with second order terms, can be ignored. It is why classical N-S equations arenpsilat closed when they are used to analyze turbulent flow. On the basic, the second order accuracy N-S equations for incompressible fluid were derived.