Bubble nucleation algorithm for the simulation of gas evolving electrodes

We propose a bubble nucleation algorithm to link a Lagrangian bubble tracker to the multi-ion transport and reaction model. This algorithm computes the bubble growth rate and the surface blocking effect at nucleation sites.     

Computing Riemann theta functions

The Riemann theta function is a complex-valued function of complex variables. It appears in the construction of many (quasi-)periodic solutions of various equations of mathematical physics. In this paper, algorithms for its computation are given. First, a formula is derived allowing the pointwise approximation of Riemann theta functions, with arbitrary, user-specified precision. This formula is used to construct a uniform approximation formula, again with arbitrary precision.

     

A finite volume implicit time integration method for solving the equations of ideal magnetohydrodynamics for the hyperbolic divergence cleaning approach

A finite volume numerical technique is proposed to solve the compressible ideal MHD equations for steady and unsteady problems based on a quasi-Newton implicit time integration strategy. The solenoidal constraint is handled by a hyperbolic divergence cleaning approach allowing its satisfaction up to machine accuracy. The conservation of the magnetic flux is computed in a consistent way using the numerical flux of the finite volume discretization. For the unsteady problem, the time accuracy is obtained by a Newton subiteration at each physical timestep thereby converging the solenoidal constraint to steady state. We perform extensive numerical experiments to validate and demonstrate the capabilities of the proposed numerical technique.