l17 - Lecture 17: Convection and Diffusion 1 Last Time In...

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1 Lecture 17: Convection and Diffusion
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2 Last Time… In the last lecture, we Developed the least-squares method for finding cell- based gradients on unstructured meshes Looked at influence of secondary gradients in destroying boundedness Considered implementation issues, including the use of face- and cell-based data structures
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3 This Time … We will Start looking at adding convection terms to our transport equation Look at two different schemes for discretizing the convection terms » Central difference scheme » Upwind difference scheme Consider the properties of these schemes vis-à-vis » Boundedness » Stability » Accuracy
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4 Steady 2D Convection-Diffusion Equation Governing equation: Assume flow field known Assume Cartesian structured mesh
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5 Discretization As usual, integrate over control volume Apply divergence theorem, linearize source term: Nothing different so far !
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6 Discretization (Cont’d) Area vectors: Flux on east face: Flow rate on east face: Units?
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7 Diffusion Term Write as usual assuming linear profile between (E,P) etc:
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This note was uploaded on 12/29/2011 for the course ME 608 taught by Professor Na during the Fall '10 term at Purdue University-West Lafayette.

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l17 - Lecture 17: Convection and Diffusion 1 Last Time In...

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