  The mean curvature flow describes the evolution of a surface(a curve) with
normal velocity proportional to the local mean curvature. It has many
applications in mathematics, science and engineering. In this paper, we develop
a numerical method for mean curvature flows by using the Onsager principle as
an approximation tool. We first show that the mean curvature flow can be
derived naturally from the Onsager variational principle. Then we consider a
piecewisely linear approximation of the curve and derive a discrete geometric
flow. The discrete flow is described by a system of ordinary differential
equations for the nodes of the discrete curve. We prove that the discrete
system preserve the energy dissipation structure in the framework of the
Onsager principle and this implies the energy decreasing property. The ODE
system can be solved by an improved Euler scheme and this leads to an efficient
fully discrete scheme. We first consider the method for a simple mean curvature
flow and then extend it to volume preserving mean curvature flow and also a
wetting problem on substrates. Numerical examples show that the method has
optimal convergence rate and works well for all the three problems.
