This procedure, denoted Lagged Diffusivity method, computes the solution by lagging the diffusion term.
Specifically, we construct a unified hyperbolic advection diffusion system by expressing the diffusion term as a first-order hyperbolic system and simply adding the advection term to it.
This model can explain a number of our experimental observations: the effect of raising the ionic strength is that initially motor movement occurs with faster velocity, probably by increasing the diffusion term.
By combining these two methods, a numerical scheme can be constructed that resolves, with extremely high precision, the nonlinearities of the advection terms and the smooth regions of the flow generated by the diffusion terms.
For the additional state variables,, we define the following SDEs: (4) where the trajectories of the state variables are determined solely by the diffusion terms.
Significant reduction in CPU time was observed in the evaluation of the diffusion terms, while the overall time saving is simulation-dependent due to the existence of other terms, such as the chemical source term, that are not affected by the reduction in the diffusion term.
Therefore, the outer core fluid may be reasonably considered as a perfect conductor, and the process generating field variations is described by the induction equation without the diffusion term.
Because of the diffusion term introduced by the penalizing energy, there is no longer need for the upwind scheme [10, 17] as in the traditional level set methods.
The governing equations are discretized by the finite-volume method, where the diffusion term and convection term are discretized using the two-point flux approximation (TPFA) scheme and the upwind scheme, respectively.
