Boundary Element Method, viscous fluid flow, Navier equation, cavity, Elastostatics Extending Reynolds Number range in numerical simulation Of fluid flow using Boundary Element Method

With the development of computers, the application of numerical methods in solving engineering problems has increased considerably. Methods such as Finite Element Method, Finite Volume Method and Finite Difference Method can be mentioned as some. In this research a Boundary Element Method is applied for numerical simulation. The main difference among the Boundary Element method and other numerical methods is the governing mathematics. At first In this method the governing equation is integrated. This leads to a decrease in the dimensions of the problem and then the simulation is performed. In this research, by a change of variable, the Navier Stokes equation is transformed to Navier equation in Elastostatics at first. Subsequently the methods proposed for solving the problems in Elastostatics is utilized to solve the viscous fluid flow. In fact, the applied fundamental solution is the main difference among the proposed method and other Boundary Element Methods. In the proposed method, in contrast to previously proposed methods, the fundamental solution of the Navier equation is utilized for simulation. At last, by considering the governing mathematics a computer code is developed for viscous flow simulation. The code is applied to two different geometries, a lid-driven-cavity and a backward facing step. Convergent solutions is achieved up to Reynolsds numbers equal with 600 and 100 respectively.