
ISAT is a powerful tool that enables realistic chemistry to be incorporated in multidimensional flow simulations by accelerating the chemistry calculations. Typical speedups of 100fold are common. This power is apparent if one considers that with a 100fold speedup, a simulation that would take three months without ISAT can be run in one day.
At the start of a FLUENT simulation using ISAT, the ISAT table is empty. For the first reaction step, Equation 18.210 is integrated with a stiff ODE solver. This is called Direct Integration (DI). The first table entry is created and consists of:
The next reaction mapping is calculated as follows: The initial composition vector for this particle is denoted
, where the subscript
denotes a
query. The existing table (consisting of one entry at this stage) is queried by interpolating the new mapping as
The mapping gradient is hence used to linearly interpolate the table when queried. The ellipsoid of accuracy (EOA) is the elliptical space around the table point where the linear approximation to the mapping is accurate to the specified tolerance, .
If the query point is within the EOA, then the linear interpolation by Equation 18.211 is sufficiently accurate, and the mapping is retrieved. Otherwise, a direct integration (DI) is performed and the mapping error is calculated (here, is a scaling matrix). If this error is smaller than the specified error tolerance ( ), then the original interpolation is accurate and the EOA is grown so as to include . If not, a new table entry is added.
Table entries are stored as leaves in a binary tree. When a new table entry is added, the original leaf becomes a node with two leavesthe original leaf and the new entry. A cutting hyperplane is created at the new node, so that the two leaves are on either side of this cutting plane. A composition vector will hence lie on either side of this hyperplane.
The ISAT algorithm is summarized as follows:
At the start of the simulation, most operations are adds and grows. Later, as more of the composition space is tabulated, retrieves become frequent. Since adds and grows are very slow whereas retrieves are relatively quick, initial FLUENT iterations are slow but accelerate as the table is built.