We propose a second order, fully semi-Lagrangian method for the numerical solution of systems of advection-diffusion-reaction equations, which is based on a semi-Lagrangian approach to approximate in time both the advective and the diffusive terms. The proposed method allows to use large time steps, while avoiding the solution of large linear systems, which would be required by implicit time discretization techniques. Standard interpolation procedures are used for the space discretization on structured and unstructured meshes. A novel extrapolation technique is proposed to enforce second-order accurate Dirichlet boundary conditions. We include a theoretical analysis of the scheme, along with numerical experiments which demonstrate the effectiveness of the proposed approach and its superior efficiency with respect to more conventional explicit and implicit time discretizations.

我们提出了一种二阶全半拉格朗日方法，用于对流-扩散-反应方程系统的数值解，该方法基于半拉格朗日方法来在时间上逼近对流项和扩散项。所提出的方法允许使用大的时间步长，同时避免了隐式时间离散化技术所需的大型线性系统的解决方案。标准插值程序用于结构化和非结构化网格的空间离散化。提出了一种新的外推技术来强制执行二阶精确 Dirichlet 边界条件。我们包括对该方案的理论分析，