Convergence of five‐point scheme with diagonally dominant characteristic for DLR k−ε model and its application

Abstract

In this paper, the equivalent equations of DLR k − turbulent model in the boundary-fitted curvilinear coordinate are employed. Using the upwind idea that the contribution of the difference coefficients to the main node is positive contribution, and the other nodes are negative contribution or no contribution, new five-point difference schemes with a full diagonally dominant coefficient matrix (5-point-DD difference scheme) are constructed. Finally, taking the u equation in the DLR k− turbulent model as an example, the mathematical characteristics of the 5-point-DD difference scheme are analyzed, and the uniform boundedness and convergence theorems of the Gauss-Seidel iterative sequence are given. Numerical simulations show that the five-point schemes are strictly diagonally dominant, and the calculated results are in good agreement with the experimental results. KEYWORDS conical diffuser, convergence, DLR k − turbulent model, strictly diagonally dominant matrix, 5-point-DD difference scheme Int J Numer Meth Fluids. 2020;92:189-211.wileyonlinelibrary.com/journal/fld