We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include flux-corrected transport schemes and monolithic limiters. We discretize in space using a continuous Galerkin method and P1 or Q1 finite elements. Time integration is performed using the Crank-Nicolson method or an explicit strong stability preserving Runge-Kutta method. Nonlinear systems are solved using a fixed-point iteration method, which requires solution of large linear systems at each iteration or time step. The great variety of options in the choice of discretization methods and solver components calls for a dedicated comparative study of existing approaches. To perform such a study, we define new 3D test problems for time dependent and stationary convection-diffusion-reaction equations. The results of our numerical experiments illustrate how the limiting technique, time discretization and solver impact on the overall performance.

中文翻译：

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对流-扩散-反应方程的代数稳定离散化求解器的评估

我们考虑 3D 对流主导的传输问题的通量校正有限元离散化，并基于这种近似评估算法的计算效率。正在研究的方法包括通量校正传输方案和单片限制器。我们使用连续 Galerkin 方法和 P1或问1有限元。使用 Crank-Nicolson 方法或显式强稳定性保持 Runge-Kutta 方法执行时间积分。非线性系统使用定点迭代方法求解，该方法需要在每个迭代或时间步长求解大型线性系统。离散化方法和求解器组件的选择多种多样，需要对现有方法进行专门的比较研究。为了进行这样的研究，我们为时间相关和静止的对流-扩散-反应方程定义了新的 3D 测试问题。我们的数值实验结果说明了限制技术、时间离散化和求解器如何影响整体性能。