The College of Science in the Department of Mathematics discussed a Ph.D. thesis entitled Advanced Numerical Algorithms for Simulating Thermal Non-Newtonian Fluids in Fixed and Free Surface Flows for postgraduate student Bashaer K. Jasim. This thesis presents advanced numerical algorithms developed to analyze incompressible, non-isothermal, non-Newtonian fluid flows using two distinct approaches: The first is the Taylor–Galerkin / Pressure Correction algorithm, and the second is the Taylor–Galerkin / Extended Artificial Compressibility algorithm. Both of them employed the Galerkin finite element method for spatial discretization and a two-step temporal discretization based on the Lax-Wendroff scheme.
To better capture the realistic behavior of inelastic fluids, the study includes temperature-dependent viscosity and viscous dissipation in the energy equation. The strong coupling of these effects makes the governing equations more complex, requiring algorithms characterized by high accuracy and efficiency.