Nodal integral method for convection-diffusion transport using linear and higher order quadrilateral elements

Abstract

Generic nodal integral method (NIM) based scheme, utilizing nine noded 2D quadratic elements along with four noded 2D linear elements, is developed to solve the fluid flow and heat transfer equations in complex geometries. Non-linear (quadratic) quadrilateral elements are used for discretization of boundary region and linear quadrilateral elements are used for interior region. Lagrange interpolation functions are used to map both type of elements to corresponding square computational elements. The scheme for Neumann and mixed type of boundary conditions are also developed for quadratic elements. C1 type continuity condition is imposed at the interfaces of adjacent elements. Numerical results are compared with analytical solutions for diffusion and advection-diffusion equations. Results for Navier–Stokes equations in curved domain are compared with previously reported experimental as well as numerical results. The comparative study has also been done between presently developed scheme using quadratic and linear elements (referred as scheme-1) and scheme based on complete discretization with linear elements (referred as scheme-2). The comparison shows that both the schemes are of nearly second order accurate while the scheme-1 is more accurate than scheme-2. The results show that the efficient mapping of curved surface with quadratic elements improves the accuracy of NIM schemes.