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row1. row2. a. Grid. row3. row4. col1 col2 col3 col4. i. b. Mesh. c. Cloud. i. A control volume solution based on an unstructured mesh (Linear Triangular Elements). Control Volume Finite Element CVFE Method. We will use our standard steady state test problem.

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  1. row1 row2 a. Grid row3 row4 col1 col2 col3 col4 i b. Mesh c. Cloud i A control volume solution based on an unstructured mesh (Linear Triangular Elements) Control Volume Finite Element CVFE Method We will use our standard steady state test problem With boundary conditions Can readily handle arbitrary domains First let us outline the basic ideas

  2. i i,2 i,3 i,1 i i,4 i i,7 i,6 i,5 Region of Support Control Volume First Geometric features Or in more detail

  3. element f2 f1 nf1 j = 1 or 5 k = Si,1 or Si,5 j = 4 k = Si,4 internal node Ni = 4 i j = 3 k = Si,3 j = 2 k = Si,2 support control volume j = 4 k = Si,4 Si,,5 = 0 j = 3 k = Si,3 boundary node i Ni = 4 j = 1 k = Si,1 j = 2 k = Si,2

  4. j = 1 or 5 k = Si,1 or Si,5 j = 4 k = Si,4 internal node Nis = 4 i j = 3 k = Si,3 j = 2 k = Si,2 support control volume For control volume shown our governing equation can be written as Length of face Calculate this From node value In element element n The element shown will contribute to the coefficients

  5. The task calculate this quantity In terms of nodal values of T At the mid point Of each of the faces Of the control volume 3 2 Two bits of information needed 1. The linear interpolation in the element via the shape function Note we can approximate the continuous variable in the element as So in element unknown function is a planar surface. Note a, b and c are constants chosen such that values of T are piecewise (C0) continuous between elements --“reptile skin” approximation See Shape Function notes---from web—shape.pdf

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