19.3. MSMD Solution Method: Coupling Between CFD and Submodels

In theory, an electrochemical submodel could be constructed and solved for every CFD cell at every flow iteration (for steady simulations) or timestep (for transient simulations). For the ECM model, this results in solving a set of four algebraic differential equations. For the Newman model, this can involve solving a system of hundreds of algebraic differential equations, depending upon the number of discretization points used in the electrode and particle domain. This adds to a tremendous computational cost of the simulation. In practice, the submodel, especially the Newman's P2D model, is typically constructed for a group of cells, called a cluster.

The idea of cell clustering comes from the fact that the current transfer rate, , is more or less uniform, although current itself is not. As a result, instead of solving the submodel for every computational cell, we can group CFD cells into clusters and solve the submodel only once for each cluster.

Ansys Fluent provides a tool for grouping the CFD cells into clusters. For a user-specified number of clusters Nx, Ny, and Nz in the X, Y, and Z directions respectively, the solver will divide the battery electrochemical domain into NxNyNz clusters and then obtain the solution for each cluster using the cluster-average values.