A development of high resolution NFT model for simulation of incompressible flows is presented. The model uses finite volume spatial discretisation with edge based data structure and operates on unstructured meshes with arbitrary shaped cells. The key features of the model include non-oscillatory advection scheme Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) and non-symmetric Krylov-subspace elliptic solver.
The NFT MPDATA model integrates the Reynolds Average Navier Stokes (RANS) equations. The implementation of the Spalart-Allmaras one equations turbulence model extends the development further to turbulent flows. An efficient non-staggered mesh arrangement for pressure and velocity is employed and provides smooth solutions without a need of artificial dissipation. In contrast to commonly used schemes, a collocated arrangement for flow variables is possible as the stabilisation of the NFT MPDATA scheme arises naturally from the design of MPDATA. Other benefits of MPDATA include: second order accuracy, strict sign-preserving and full multidimensionality.
The flexibility and robustness of the new approach is studied and validated for laminar and turbulent flows. Theoretical developments are supported by numerical testing. Successful quantitative and qualitative comparisons with the numerical and experimental results available from literature confirm the validity and accuracy of the NFT MPDATA scheme and open the avenue for its exploitation for engineering problems with complex geometries requiring flexible representation using unstructured meshes.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.