Error Estimations for Flow Characterization With Numerical and Analytical Solutions

Use of radial basis functions(RBFs) in the numerical solution of partial differential equations has gained popularity as it is meshless and can readily be extended to multi-dimensional problems. RBFs have been used in different context and emerged as a potential alternative for numerical solution of PDEs. In this article, a Flow Between Parallel Plates problem was solved using a Multiquadric Radial Basis Function Collocation Method (MQ-RBFCM), then, the results were compared with the analytic ones and the root mean square of the errors between the model and analytic results were calculated. Numerical results are presented for 5 different cases, where the number of inputs or definitions are increased to see whether changing the number of points makes the results better or not. Also, the absolute errors between the results were calculated to have a 3D model of the error rates and this has proven for which cases the MQ-RBFCM are better. As a result, RBF is shown to produce accurate results while requiring a much-reduced effort in problem preparation in comparison to traditional numerical methods.