Search results

For a partial differential equation with a fourth-order derivative such as the Cahn-Hilliard equation, it is always a challenge to design numerical schemes that can handle the restrictive time step introduced by this higher order term. The purpose of this paper is to employ a fractional splitting method to isolate the convective, the nonlinear second-order and the fourth-order differential terms.

The full equation is then solved by consistent schemes for each differential term independently. In addition to validating the second-order accuracy, the authors will demonstrate the efficiency of the proposed method by validating the dissipation of the Ginzberg-Lindau energy and the coarsening properties of the solution.

The scheme is second-order accuracy, the authors will demonstrate the efficiency of the proposed method by validating the dissipation of the Ginzberg-Lindau energy and the coarsening properties of the solution.

The authors believe that this is the first time the equation is handled numerically using the fractional step method. Apart from the fact that the fractional step method substantially reduces computational time, it has the advantage of simplifying a complex process efficiently. This method permits the treatment of each segment of the original equation separately and piece them together, in a way that will be explained shortly, without destroying the properties of the equation.

The purpose of this paper is to access performance of existing computational techniques to model strongly non‐linear coupled thermo‐electric problems.

A thermistor is studied as an example of a strongly non‐linear diffusion problem. The temperature field and the current flow in the device are mutually coupled via ohmic heating and very rapid variations of electric conductivity with temperature and applied electric field, which makes the problem an ideal test case for the computational techniques. The finite volume fully coupled and fractional steps (splitting) approaches on a fixed computational grid are compared with a fully coupled front‐fixing method. The algorithms' input parameters are verified by comparison with published experiments.

It was found that fully coupled methods are more effective for non‐linear diffusion problems. The front fixing provides additional improvements in terms of accuracy and computational cost.

This paper for the first time compares in detail advantages and implementation complications of each method being applied to the coupled thermo‐electric problems. Particular attention is paid to conservation properties of the algorithms and accurate solutions in the transition region with rapid changes in material properties.