In this article, we propose novel boundary treatment algorithms to avoid order reduction when implicit-explicit Runge-Kutta time discretization is used for solving convection-diffusion-reaction problems with time-dependent Di\-richlet boundary conditions. We consider Cartesian meshes and PDEs with stiff terms coming from the diffusive parts of the PDE. The algorithms treat boundary values at the implicit-explicit internal stages in the same way as the interior points. The boundary treatment strategy is designed to work with multidimensional problems with possible nonlinear advection and source terms. The proposed methods recover the designed order of convergence by numerical verification. For the spatial discretization, in this work, we consider Local Discontinuous Galerkin methods, although the developed boundary treatment algorithms can operate with other discretization schemes in space, such as Finite Differences, Finite Elements or Finite Volumes.

翻译：本文针对含时变狄利克雷边界条件的对流-扩散-反应问题，在使用隐显式Runge-Kutta时间离散方法求解时，提出了新颖的边界处理算法以避免精度阶数下降。我们考虑笛卡尔网格及偏微分方程中由扩散项产生的刚性项。该算法以与内部点相同的方式处理隐显式内部阶段的边界值。所设计的边界处理策略适用于可能包含非线性对流项和源项的多维问题。通过数值验证，所提方法恢复了设计收敛阶。在空间离散方面，本文采用局部间断Galerkin方法，但所发展的边界处理算法也可与其他空间离散方案（如有限差分法、有限元法或有限体积法）结合使用。