| In this thesis, we have studied the development and assessment of a multi-scale Computational Fluid Dynamics (CFD) model for simulating thermally driven flows. Using a constant eddy viscosity model, mean momentum and energy equations, an urban heat island circulation is derived. To resolve the localized spatial features of such a circulation, we have studied the use of an adaptive mesh method based on wavelet transformation. We have proposed a second order fully implicit time integration scheme such that the momentum and the energy equations are solved simultaneously on an adaptive collocated grid. At each time step, a system of nonlinear equations is solved using a multi-scale method, where we have used a Krylov method for improving the rate of convergence, which is a distinct feature of the proposed CFD model. To the best of our knowledge, this is the first time attempt to use an adaptive mesh and a Krylov method to optimize a multi-scale solver for heat island circulation.;With a brief presentation of the scientific problem and the methodology in Chapters 1-3, the performance of the proposed model has been verified in Chapters 4-5, where we have simulated a shear-driven flow, a thermally driven natural convection flow, and a heat island circulation. We have found that our numerical results agree well with previously published benchmark simulation results of similar flows. First, the numerical error is proportional to the given tolerance. Second, a large CFL number does not affect the accuracy significantly. Finally, the computational cost grows linearly with the number of grid points if the mesh is refined locally. The proposed model is a novel contribution to the field of mesoscale meteorology, which would help for further development of multiscale meteorological modelling. |
