Using Collocation Discrete Least Squares Meshless method in solving governing equations for non-Newtonian fluids by Herschel- Bulkley model

 One of the meshless methods is Discrete Least Squares Meshless (DLSM) method in which, the nodal points are used for estimating the shape functions and discretization of equations. Collocation Discrete Least Squares Meshless (CDLSM) method is formed by adding points as collocation points which are used in discretization of equations. In this research, Radial Point Interpolation Method (RPIM) has been used to estimate the shape functions in solving governing equations of two-dimensional non Newtonian fluid. Herscel-Bulkley model is used to simulate rheological behavior of fluid. Verification tests are achieved by three experimental bebch marks such as flow between two parallel plates, lid driven square cavity and lid-driven arc-shape cavity for Re=100. Mean square error (MSE) is determined between the numerical and experimental results and conducted to 7.1×〖10〗^(-5), 1.3×〖10〗^(-6), 1.6×〖10〗^(-6) for the three mentioned problems, respectively. The computational time consumed for simulating the lid driven square cavity problem was 1000 seconds, respectively. Also, solving lid-driven arc-shape cavity problem for each iteration took 0.65 seconds, respectively.