Interdisciplinary Applied Mathematics

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Shardlow’s Splitting Method


Another approach, which is often used in classical computational fluid dynamics, is operator splitting. In (Shardlow, 2003), the conservative forces were separated from the dissipative and random forces. First, the conservative components are computed using the classical MD approach, and subsequently the dissipative and random contributions are handled using a Langevin formulation. Two splitting schemes were developed (S1 and S2) corresponding to first-order and second-order accuracy, respectively. S1 is more efficient and is presented below.

















   Compute physical quantities.


Lowe’s Alternative Method


The approach by Lowe differs from all other integration approaches of the DPD scheme. Here, the integration of the dissipative and random forces is bypassed. Specifically, Newton’s equation of motion are integrated first, and then the system is thermalized as follows:

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