The MSMD method needs to solve two potential equations (Equation 19–4). Although the equations do not have transient terms, they are solved repeatedly during each time step in a transient fashion due to the time-varying electric load condition and the change of state of a battery charge.

However, under the following two conditions, the solution of these two potential equations can be easily found without solving them repeatedly:

A careful examination of Equation 19–4 and their boundary conditions reveals that the two equations become homogeneous linear partial differential equations under those two conditions. Instead of solving them at each time step, a scaling procedure can be used, so that the two potential fields under any electric load condition can be obtained from a reference potential field. The reference potential field can be pre-calculated at a reference load condition. By using this method, the need to solve the two potential equations at each CFD time step is eliminated entirely. The cost of a general electrochemical-thermal coupled simulation is reduced to that of a pure thermal simulation. This can save a significant amount of computational time in a battery simulation.