Chemistry Acceleration

You can use Clustering, ISAT, or Dynamic Mechanism Reduction methods to speed up Complex Chemistry calculations.

The following are chemistry acceleration options:

  • Clustering
  • In Situ Adaptive Tabulation (ISAT)
  • Dynamic Mechanism Reduction

The Relax to Chemical Equilibrium model is not an acceleration option, however, you can use it to provide a quick approximate solution for detailed chemistry computations. See Relax to Chemical Equilibrium.

Clustering

The clustering method groups cells with similar thermal and chemical states before integrating the averaged state for the group. The reaction mapping is then interpolated back to the cells assuming the net reaction rate of all cells in the cluster is the same as the cluster average.

Clustering usually provides a substantial speed-up as the number of clusters is less than the number of cells in the simulation. Since the number of clusters increases much slower than the number of cells, clustering performance improves with mesh size.

The clustering algorithm uses a uniform N-dimensional grid, where N is the number of clustering variables. The cells in the simulation are then binned into each clustering grid. By default, Simcenter STAR-CCM+ uses three clustering variables for unsteady simulations, namely equivalence ratio, temperature, and mass fraction of OH. For steady-state simulations, the log of the chemical time scale is used as an additional clustering variable.

Simcenter STAR-CCM+ provides other user-selectable clustering variables, including other species mass fractions, mixture fraction, pressure, enthalpy, and entropy.

The default clustering variables of equivalence ratio and temperature represent the underlying trajectory of mixing followed by reaction. These default clustering variables are suitable for most hydrocarbon combustors. However, there are cases where careful selection of additional clustering variables can improve accuracy. For example, for slowly forming NO formation behind a premixed flame front, where the equivalence ratio and temperature are nearly uniform, you can add the NO species mass fraction to the clustering variables list. For supersonic combustion with shock-waves, you can include the pressure variable since the pressure changes substantially through the domain.

You can view the clusters that Simcenter STAR-CCM+ generates by visualizing the Clustering Index. Each cluster has its own unique index, with the maximum value representing the total number of clusters. A Clustering Index of zero represents cells that are excluded from the reaction, such as cells with temperatures that are below the Minimum Temperature that is required for reactions. The Clustering Equivalence Ratio and Clustering Mixture Fraction are also available for post-processing.

In Situ Adaptive Tabulation (ISAT)

In Situ Adaptive Tabulation (ISAT) is a tabulation method in which computationally expensive functions are tabulated and then interpolated at run time. In this case, the stiff chemistry ODEs (ordinary differential equations) are tabulated. If there are many thermo-chemical states that are similar in time and/or space, ISAT can reduce simulation times. ISAT can substantially speed up complex chemistry simulations for steady state problems (including unsteady LES of steady combustion) in which the tabulated chemistry mappings are regularly retrieved and mechanisms have less than 40 species. However, it is not recommended to use the ISAT method for complex chemistry internal combustion engine (ICE) simulations due to the fluctuations in chemical states such as pressure.

Dr. Stephen B. Pope developed the ISAT method [766].

The ISAT tables are created at a constant pressure and time-step. If the pressure or time-step in the domain varies (as occurs in steady simulations), the ISAT solver bins the pressure and time-step values into appropriate ranges automatically, creating one table per bin.

The ISAT method approximates the solution of the ODE for a given initial condition through:
  • The thermodynamic variable (sensible enthalpy)
  • The composition variable (specific molar number)
  • The absolute pressure and time-step (depending on the type of simulation)
You can use ISAT to retrieve approximate values for multi-dimensional functions that are expensive to compute. In reacting simulations, you can use ISAT to store and retrieve approximate reaction mapping solutions from a system of coupled ODEs. During the chemistry step, the ISAT solver computes the reaction mapping in a particular cell. ISAT searches the table for an existing point with which to approximate the reaction mapping within the specified error tolerance. If ISAT finds such a point, then the new reaction mapping is not calculated with the CVODE solver, but rather interpolated based on the stored reaction mapping in the table. Otherwise, if ISAT cannot find a suitable point in the table, the CVODE solver is called, and a reaction mapping for this point is calculated. This newly calculated point is stored in the table. The size of the table therefore grows as the simulation progresses. See Complex Chemistry.

Dynamic Mechanism Reduction

When using the Complex Chemistry model, you can choose to allow the CVODE solver in Simcenter STAR-CCM+ to solve for a reduced number of species that are taken from the full chemical mechanism that is imported. The mechanism is reduced dynamically—in every cell at every time-step or iteration. Solving for fewer species reduces computational time, however, accuracy is also reduced. Dynamic Mechanism Reduction is based on the Directed Relation Graph (DRG) algorithm [755] where species that do not change any other species substantially over the each time-step or iteration are eliminated from the mechanism. See Dynamic Mechanism Reduction.

You provide the inputs for the DRG algorithm—a tolerance and a small set of target species, which are retained in the mechanism. If the species, NO, is present in a mechanism, it is automatically included in the target species.