The course is intended particularly for students that deal with continuum fluid modeling within their dissertation. The course introduces computational methods used in hydrodynamics: - Computational Fluid Dynamics (CFD): introduction, its history and content of the subject - Basic overview of vector calculus: vector, matrices and tensors, basic vector calculus theorems - Mathematical description of physical phenomena, Euler and Lagrange descriptions of conservation laws, mass, heat and momentum balance, fluid flow characteristics, dimensionless forms of balance equations ? Discretization process ? general description: finite difference method, finite volume method, finite element method, domain discretization, discretization of equations, solution of discretization equations - Spatial discretization of diffusion and convection terms, time discretization, source term discretization - Solving algebraic equations: direct and iterative methods, multigrid methods - Algorithms for incompressible and compressible fluid flow ? basic problems, discretization of Navier-Stokes equations and continuity equation, staggered and collocated networks, pressure correction method, SIMPLE, SIMPLEC, PRIME and PISO algorithm - Turbulent flow modeling: laminar flow vs. turbulent flow, direct numerical simulation method (DNS), large eddy methods (LES), Reynolds-averaged Navier-Stokes model (RANS) - Modeling of non-Newtonian fluids: basic rheological models, influence of non-Newtonian fluids on the flow characteristics - Modeling of multiphase flow by using hierarchical methods based on multiple scale principles of reality description (models describing flow at different levels of detail)
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