Numerical Solution to Coupled Burgers' Equations by Gaussian-Based Hermite Collocation Scheme

摘要

One of the most challenging PDE forms in fluid dynamics namely Burgers equations is solved numerically in thiswork. Its transient, nonlinear, and coupling structure are carefully treated. The Hermite type of collocation mesh-freemethod is applied to the spatial terms and the 4~(th)-order Runge Kutta is adopted to discretize the governing equations in time.Themethod is applied in conjunction with the Gaussian radial basis function. The effect of viscous force at high Reynolds number up to 1,300 is investigated using the method. For the purpose of validation, a conventional global collocation scheme (also known as "Kansa" method) is applied parallelly. Solutions obtained are validated against the exact solution and alsowith some other numericalworks available in literature when possible.