METHOD FOR SOLVING THE NAVIER-STOKES EQUATION

摘要

A method for simulation of frequency-dependent friction in laminar flow fluids in pipes is disclosed. The following steps are carried out: establishment of a motion equation for fluids, depending on a first position- and time-dependent fluid parameter (v) and a second position- and time-dependent fluid parameter (P), establishment of a continuity equation for fluids, dependent on the first (P)and the second (v) fluid parameter, expansion of the first fluid parameter (P) in at least one time-independent base (Z, J) and a first time-dependent coefficient (pSUBm/SUB), said base (Z, J) comprising a set of functions, expansion of the second fluid parameter (v) in at least one of the time-independent bases (Z,J) and in a second time-dependent coefficient (vSUBk,m/SUB), application of both expansions in the motion equation and the continuity equation, scalar multiplication of each equation by at least one function from at least one base (Z, J), such as to give a regular system of first-order differential equations with coefficients (A, B) for the time-dependent coefficients (pSUBm/SUB, vSUBk,m/SUB), calculation of the coefficients (A, B) for a given time (t), at least one of the two time-dependent coefficients (pSUBm/SUB, vSUBk,m/SUB) meets at least one constraint and integration of the differential equation over the time-dependent first and second coefficients, whereby the constraint is met.