论文标题
关于非线性漂移扩散方程的平方根近似有限体积方案
On the square-root approximation finite volume scheme for nonlinear drift-diffusion equations
论文作者
论文摘要
我们研究了一个有限的体积方案，用于近似于非线性对流和罗宾边界条件的对流扩散方程。该方案建立在对这种连续方程式的解释为基础上，例如某些简单的排除跳跃过程的流体动力限制。我们表明该方案承认了一个独特的离散解决方案，即保留解决方案上的自然界限，并且它编码了热力学的第二个原理，即在时间沿时间消散一些自由能。因此，由于紧凑的论点，该方案的融合被严格确定。最终提供了数值模拟，突出了该方案的整体良好行为。
We study a finite volume scheme for the approximation of the solution to convection diffusion equations with nonlinear convection and Robin boundary conditions. The scheme builds on the interpretation of such a continuous equation as the hydrodynamic limit of some simple exclusion jump process. We show that the scheme admits a unique discrete solution, that the natural bounds on the solution are preserved, and that it encodes the second principle of thermodynamics in the sense that some free energy is dissipated along time. The convergence of the scheme is then rigorously established thanks to compactness arguments. Numerical simulations are finally provided, highlighting the overall good behavior of the scheme.
