NODAL INTEGRAL METHOD FOR COMPLEX GEOMTRIES USING HIGHER ORDER ELEMENTS
A novel numerical scheme utilizing f our noded linear and
nine noded non-linear quadrilateral elements is developed to
solve the governing fluid flow and heat transfer equations in complex domains. Non-linear elements are used in discretization of boundary regions and linear-elements are used for inner domain. Lagrange interpolation functions are used for bijective mapping of these type of elements to corresponding square computational elements. Implementation of Dirichlet boundary conditions are straight forward, while for Neumann and mixed type of boundary conditions, a generic scheme is developed by piecewise linearization
of quadratic surface of non-linear elements. C1 type continuity condition is imposed at the interfaces of adjacent elements. Numerical results are compared with analytical solutions for both Diffusion and Advection-Diffusion equations. L2 norm errors are also calculated for quantitative analysis of developed numerical schemes. The results show that the efficient mapping of curved surface with quadratic elements improves the accuracy
of NIM schemes.