Abstract
A new variable time step method, which is called the backwards calculating time step method, is presented in this paper. It allows numerical simulation of soil freezing and thawing while avoiding “phase change missing and overflowing”. A sensitive heat capacity model is introduced through which the calculation errors are analyzed. Then the equation using the self-adjusted time step is presented and solved using finite differences. Through this equation, the time needed for a space cell to reach the phase change point temperature is calculated. Using this time allows the time step to be adjusted so that errors caused by “phase change missing and overflowing” are successfully eliminated. Above all, the obvious features of this method are an accelerated rate for adjusting the time step and simplifing the computations. An actual example proves that this method can accurately calculate the temperature fields during soil freezing and thawing. It is an improvement over traditional methods and can be widely used on complicated multi-dimensional phase change problems.
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