Alternative solution algorithm for coupled thermal-hydraulic problems

A thermal-hydraulic system involves flow of a fluid for which a combined solution of the continuity, momentum, and energy equations is required. When the solutions of the energy and momentum fields are dependent on each other, the system is said to be thermally coupled. A common problem encountered in the numerical solution of strongly coupled thermal-hydraulic problems is a very slow rate of convergence or a complete lack of convergence. Many times this degradation in convergence is due to the lack of true coupling between the energy and momentum fields during the iteration process. In the most widely used solution algorithms - such as the SIMPLE algorithm and its many variants - a sequential solution technique is required. That is, the solution process alternates between the flow and energy fields until a converged solution is obtained. This approach allows only implicit energy-momentum coupling. To improve the convergence rate for strongly coupled problems, a practical solution algorithm that can accommodate true energy-momentum coupling terms was developed. A complete simultaneous (versus sequential) solution of the governing conservation equations utilizing a line-by-line solution was developed and direct coupling terms between the momentum and energy fields were added utilizing a modified Newton-Raphson technique