Numerical method for coupled fluid flow, heat transfer and stress analysis using unstructured moving meshes with cells of arbitrary topology Original Research Article

A numerical method is presented that can be used for both solid body stress analysis and fluid flow predictions, independently as well as in a coupled manner. The method uses an integral form of equations governing mass, energy and momentum balance for an arbitrary control volume. A detailed description is provided of a novel second-order accurate spatial discretisation technique which can accommodate unstructured moving meshes with cells of arbitrary topology. This is accompanied by a fully implicit temporal discretisation, which makes the method stable for any time step size. The resulting set of coupled non-linear algebraic equations is solved by employing a segregated approach, leading to a decoupled set of linear algebraic equations for each dependent variable, with a sparse diagonally dominant coefficient matrix. These equations are solved by an iterative conjugate gradient solver which retains the sparsity of the coefficient matrix, thus achieving a very efficient use of computer resources.