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August 17, 2001, 00:57 
Determinant in ICEMCFD and Fluent

#1 
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Hi all,
I would like to know firstly the exact definition and the physical meaning of the determonant of a cell as used by ICEMCFD for checking the quality of a CELL. in a domain. But in Fluent the measure used is Volumes. How are they corelated? Thanks for your time. Regards, Anandanth 

August 17, 2001, 07:10 
Re: Determinant in ICEMCFD and Fluent

#2 
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Hello,
Here is the spec for ICEM CFD's determinat quality. You will have to ask Fluent for their spec. However if you have a negative det. the you will have negative volumes. There is only one special case of a 4 sided triangle that measures 0 on the det. quality but will still run in Fluent. Try to aim for 0.2 det. in ICEM and will have no problems in the solution. You can get away with 0.01 det. if you have a complex piece of CAD. regards David ICEM CFD UK  Calculate the determinants (volume measure) of all elements. This works for structured volume and surface meshes, as well as for HEXA_8 (linear hexahedral) and QUAD_4 (linear quadrilateral) elements. The determinant of an element is calculated from its Jacobian matrix, and is a normalized measure of the element's volume, computed at each corner node. For an ideal mesh element, the determinant of the Jacobian is the same at all four corners (for example, parallelepipeds have this property). Given a subregion of a brick element, we call its volume an inner volume of the mesh. The sign of any inner volume is dependent on the sign of the determinant of the Jacobian. A determinant of 100 corresponds to an element all of whose sides are parallel. A determinant greater than 0 corresponds to one that has no negative internal volume. The algorithm for calculating the Determinant is as follows: Calculate the Jacobians of the 27 canonical points of the trilinear hexahedron, A(j, k, l), for j, k, and l = 1, 2, 3. Find a point (j, k, l) where the value det(A(j, k, l)) achieves a maximum, and define mx by mx = max(det(A(j, k, l))). If mx is 0, then the brick is empty. The determinant will be 0 in this case. Find the value m = max (det(A(j, k, l))  mx / mx). The determinant is defined as 100 * (1  m). If the value of det(A(j, k, l)) changes sign, then m will be greater than 1. Such brick elements are the ones that have negative internal volumes. For example, if a cube is distorted by moving one corner towards the center until the volume is no longer convex, i.e., the corner was pushed beyond the plane defined by its three adjacent corners, then the distorted brick will have a negative internal volume. The value m is invariant under translation, scaling, and rotation of the brick element. 2D elements are treated in a similar fashion, where mx is given by mx = max(N(j, k)2), and N(j, k)2 is the squared norm of the normal vector to the point (j, k) for j and k = 1, 2, and 3. The second difference is that in part 3, m is given by m = max (dot(N(j, k), N(j_mx, k_mx))/mx). where dot() is the dot product of the two vectors. The maximum is taken over the canonical points such that N(j_mx, k_mx)2 = mx. The determinant is defined as 100 * m. 

August 17, 2001, 23:53 
Re: Determinant in ICEMCFD and Fluent

#3 
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If I remember correctly from my finite element classes. That if you transform an arbitrary volume to another then the determinant of the Jacobian of the transformation is the ratio of the new cell volume to the old cell volume.


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