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<p>With zero-flux boundary conditions imposed at both ends, amounts of components in a system cannot change as a result of a unidimensional diffusion in it. With appropriately chosen time steps, the Crank-Nicolson scheme can dependably track a temporal evolution of an initial discrete concentration profile, but an invariance of an area below a continuously changing concentration <i>vs.</i> position curve is not guaranteed. In this work, a heuristic yet mathematically sound technique of incorporating a "constant integral" requirement into the Crank-Nicolson method is proposed.</p>

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Mass-Preserving Modeling of Diffusion in a Closed System

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • Dmitri V. Malakhov

摘要

With zero-flux boundary conditions imposed at both ends, amounts of components in a system cannot change as a result of a unidimensional diffusion in it. With appropriately chosen time steps, the Crank-Nicolson scheme can dependably track a temporal evolution of an initial discrete concentration profile, but an invariance of an area below a continuously changing concentration vs. position curve is not guaranteed. In this work, a heuristic yet mathematically sound technique of incorporating a "constant integral" requirement into the Crank-Nicolson method is proposed.