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首页> 外文期刊>Discrete and continuous dynamical systems >ENERGETIC VARIATIONAL APPROACH IN COMPLEX FLUIDS: MAXIMUM DISSIPATION PRINCIPLE
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ENERGETIC VARIATIONAL APPROACH IN COMPLEX FLUIDS: MAXIMUM DISSIPATION PRINCIPLE

机译：复杂流体中的能量变化方法：最大耗散原理

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摘要

We discuss the general energetic variational approaches for hydro-dynamic systems of complex fluids. In these energetic variational approaches, the least action principle (LAP) with action functional gives the Hamilton-ian parts (conservative force) of the hydrodynamic systems, and the maximum/minimum dissipation principle (MDP), I.e., Onsager's principle, gives the dissipative parts (dissipative force) of the systems. When we combine the two systems derived from the two different principles, we obtain a whole coupled nonlinear system of equations satisfying the dissipative energy law. We will discuss the important roles of MDP in designing numerical method for computations of hydrodynamic systems in complex fluids. We will reformulate the dissipation in energy equation in terms of a rate in time by using an appropriate evolution equations, then the MDP is employed in the reformulated dissipation to obtain the dissipative force for the hydrodynamic systems. The systems are consistent with the Hamiltonian parts which are derived from LAP. This procedure allows the usage of lower order element (a continuous C~0 finite element) in numerical method to solve the system rather than high order elements, and at the same time preserves the dissipative energy law. We also verify this method through some numerical experiments in simulating the free interface motion in the mixture of two different fluids.
机译：我们讨论了复杂流体流体动力系统的一般能量变分方法。在这些高能变分方法中，具有作用函数的最小作用原理（LAP）给出了流体动力学系统的汉密尔顿量（保守力），最大/最小耗散原理（MDP）即Onsager原理给出了耗散性系统的零件（耗散力）。当我们结合从两个不同原理得出的两个系统时，我们得到一个满足耗散能定律的整体耦合非线性方程组。我们将讨论MDP在设计用于计算复杂流体中的流体力学系统的数值方法中的重要作用。我们将通过使用适当的演化方程，按照时间比率重新计算能量方程中的耗散，然后将MDP用于重新计算的耗散中，以获得流体动力系统的耗散力。该系统与从LAP导出的哈密顿量一致。该程序允许在数值方法中使用低阶元素（连续的C〜0有限元）而不是高阶元素来求解系统，同时保留了耗散能定律。我们还通过一些数值实验在模拟两种不同流体的混合物中的自由界面运动中验证了该方法。

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  • 来源
    《Discrete and continuous dynamical systems》 |2010年第4期|P.1291-1304|共14页
  • 作者

    Yunkyong Hyon; Do Young Kwak; Chun Liu;

  • 作者单位

    Institute for Mathematics and Its Applications University of Minnesota Minneapolis, MN 55455, USA;

    Department of Mathematical Sciences Korea Advanced Institute of Science and Technology Daejeon 305-701, Republic of Korea;

    Department of Mathematics Pennsylvania State University University Park, PA 16802, USA;

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