Condition Monitoring a Coupled Differential Equation Using Order of Accuracy of Boundary Values in a Lid-Driven Cavity

Abstract

The unsteady vorticity-transport equation and coupled stream function equation are discretised using Crank–Nicholson scheme in a finite difference mesh. The boundary conditions following Thom’s formula, Jenison’s formula of second and third order and computational boundary method are applied to solve the coupled equations. The geometry for the problem is a lid-driven cavity in which the coupled differential equations are solved. The order of accuracy of the boundary conditions affects largely the value of vorticity values at the centre of the primary vortex. At lower Reynolds number these values don’t have any impact; however at large Reynolds numbers those values are affected by large amount. Sometimes the computed values overshot the theoretical value of vorticity i.e. − 1.88596 with increase of Reynolds number. For this computation the grid meshes 129 × 129 and 257 × 257 are used. It is also observed that the computed vorticity value remain within the theoretical limit for the Jenison’s second order, third order and computational boundary element method.