Numerical Simulation of a Lead-Acid Battery Discharge Process using a Developed Framework on Graphic Processing Units

In the present work, a framework is developed for implementation of finite difference schemes on Graphic Processing Units (GPU). The framework is developed using the CUDA language and C++ template meta-programming techniques. The framework is also applicable for other numerical methods which can be represented similar to finite difference schemes such as finite volume methods on structured grids. The framework supports both linear and nonlinear finite difference stencils. Furthermore, the arithmetic operators and math functions are overloaded to ease the array-based computations on GPUs. The reduction algorithms are also efficiently included in the framework. The discharge process of a lead-acid battery cell is simulated using the facilities provided by the framework. The governing equations are unsteady and include two nonlinear diffusion equations for solid (electrode) and liquid (electrolyte) potentials and three transient equations for acid concentration, porosity and the state of charge. The equations are discretized using the finite volume method. The framework allows the user to develop the numerical solver with a few efforts. The numerical simulation results are reported for different relations for open circuit potential and the electrolyte diffusion coefficient