Numerical Study Using Statistical and Quantum Approaches for Solving Energy and Navier Stokes Momentum Equations (PDEs)

Statistical and Quantum numerical method was implemented in this study to solve various cases in partial differential equations (PDEs) in engineering applications. One-dimensional with two lattices arrangements as well as two-dimensional with nine lattices arrangements is employed. The stability and the accuracy have been investigated either using statistical technique or using Euler’s method. The numerical limitations of using LBM method have been obtained and compared with those obtained by Euler’s method finite difference method. The main goal of this study is to investigate the ability of a statistical method in solving various ODEs or PDEs in energy and momentum equations and comparing them with those obtained by a classical numerical technique. The results show the ability of the statistical method for solving ODEs and PDE’s with more stable and accurate results. Therefore, the motivation of utilizing the statistical technique is the stability and it is easy for a complex fluid flow application.