Application of Nodal Integral Method for Convection-Diffusion Physics and Navier-Stokes Equations

Abstract

Generic nodal integral method (NIM) based scheme is being utilized to solve the diffusion, convectiondiffusion problems and navier-stokes equations in regular rectangle cartesian geometry. The problems taken into account in present work are 2D steady state diffusion with heat source, 1D steady state diffusion, 2D steady state convection-diffusion with heat source and flow in lid driven cavity with square obstacle at center. Numerical results for FDM and NIM are compared, with respect to analytical solution for diffusion and convection-diffusion problems. Different respective grid sizes have been used to capture problem flow domain for diffusion, convection-diffusion and lid driven cavity. The flow in lid driven cavity with square obstacle at center has been modelled successfully using discretized navier-stokes equations utilizing NIM. In case of diffusion and convection dominant diffusion, the NIM scheme yields far better results as compared to FDM for any given grid size and takes less computational time as contrasted with latter. For coarser meshes specifically, for most of the defined cases, the NIM converges to very low errors in comparison to FDM.i.e. approximately ten to hundred times less than latter. Due to this reason, in the present work, the NIM modelled discretized navier stokes equations has been used effectively to capture the flow profiles efficiently for lid driven cavity at any grid size, coarser or finer, for high or low reynold numbers ranging from 100 to 1000.