Lecture 5 Solution Methods Applied （讲座5应用解决方案的方法）.pdfVIP

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Lecture 5 Solution Methods Applied （讲座5应用解决方案的方法）.pdf

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Lecture 5 Solution Methods Applied （讲座5应用解决方案的方法）

Lecture 5 - Solution Methods Applied Computational Fluid Dynamics Instructor: André Bakker © André Bakker (2002-2006) 1 © Fluent Inc. (2002) Solution methods • Focus on finite volume method. • Background of finite volume method. • Discretization example. • General solution method. • Convergence. • Accuracy and numerical diffusion. • Pressure velocity coupling. • Segregated versus coupled solver methods. • Multigrid solver. • Summary. 2 Overview of numerical methods • Many CFD techniques exist. • The most common in commercially available CFD programs are: – The finite volume method has the broadest applicability (~80%). – Finite element (~15%). • Here we will focus on the finite volume method. • There are certainly many other approaches (5%), including: – Finite difference. – Finite element. – Spectral methods. – Boundary element. – Vorticity based methods. – Lattice gas/lattice Boltzmann. – And more! 3 Finite difference method (FDM) • Historically, the oldest of the three. • Techniques published as early as 1910 by L. F. Richardson. • Seminal paper by Courant, Fredrichson and Lewy (1928) derived stability criteria for explicit time stepping. • First ever numerical solution: flow over a circular cylinder by Thom (1933). • Scientific American article by Harlow and Fromm (1965) clearly and publicly expresses the idea of “computer experiments” for the first time and CFD is born!! • Advantage: easy to implement. • Disadvantages: restricted to simple grids and does not conserve momentum, energy, and mass on