13-appendix-d.md

Appendix D: Implementation of tight coupling

One of the major advantages of CAEBAT project is that the final product is an open source software. In other words the user can become a developer and implement his own simulation scenarios as well as integrate components into VIBE. In this example we discuss implementation of tight coupling (Picard iteration) between electrochemical (DualFoil) and Thermal components in VIBE.

In general, Picard iteration to a specified convergence criteria provides tight coupling of two physics components f0 and f1 exchanging variables via functions g. At each time step, a fixed-point iteration can be schematically represented as follows.

{#fig:converged width=5.0in}

In terms of implementation in VIBE, such task is relatively simple and requires creating the new simulation driver which would call the corresponding components in the right sequence until the desired convergence is reached. Drivers can be found in VIBE/trunk/components (see figure below).

{#fig:components width=1.0in}

Simulation drivers follow Python logic with the Driver class where the actual call of components is performed. The sequence and number of components are characteristic of the simulation setup. For instance the unit iteration sequence in this example can be represented as

class Driver(Component):

    def __init__(self, services, config):
        "code here"

    def step(self, timestamp=0):
        "code here"

    # Iterate throught the timeloop
    for t in tlist[1:len(timeloop)]:
        "code here"
        while abs(T_new_sum - T_old_sum) > tol :
            services.call(chartran_comp, 'init', t)
            services.call(chartran_comp, 'step', t)
            services.call(chartran_comp, 'finalize', t)

            services.call(electrical_comp, 'init', t)
            services.call(electrical_comp, 'step', t)
            services.call(electrical_comp, 'finalize', t)

            services.call(thermal_comp, 'init', t)
            services.call(thermal_comp, 'step', t)
            services.call(thermal_comp, 'finalize', t)

Where the Electrochemical (‘chartran’), Electrical and thermal components are called in the above sequence at each time step. In this particular case the convergence is checked in terms of temperatures from the current and previous Picard iteration. The thermal component is coupled to DualFoil via temperature-dependent diffusivities and Buttler-Volmer kinetics in DualFoil component. To check the influence of tight coupling, simulations were run on an unrolled cell with properties of the polymer cell described in Doyle, Fuller 1993. The results are shown in [@Fig:heat-source]. Weak dependence of sources on temperature results in very fast convergence of Picard iterations (typically within 4 iterations).

{#fig:heat-source width=5.0in}