| Abstract: |
| We propose variational integrators for the nonequilibrium thermodynamics focusing on the case of simple closed systems. The variational integrators are obtained by a variational discretization of the Lagrangian variational formulation of nonequilibrium thermodynamics, which is a natural extension of the variational discretization for Hamilton`s principle in mechanics to include irreversible processes. First we show the continuous setting of a variational formulation of the nonequilibrium thermodynamics, in which we have a structure-preserving property of the flow of the evolution equations as we have the symplectic property associated with the Euler-Lagrange equations in Lagrangian mechanics. Then, we develop the discrete analog of the variational formulation of the nonequilibrium thermodynamics and show how the discrete flow of the numerical solution also has such a structure-preserving property. In particular, we discuss the regularity condition of the discrete evolution equations, which ensures the existence of the discrete flow of the system. We finally illustrate our theory by some numerical examples of simple closed systems. |
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