Enhancing the Convergence of the Multigrid-Reduction-in-Time Method for the Euler and Navier–Stokes Equations

Excessive spatial parallelization can introduce a performance bottleneck due to the communication overhead. While time-parallel method multigrid-reduction-in-time (MGRIT) provides an alternative to enhance concurrency, it generally requires large numbers of iterations to converge or even fails when applied to advection-dominated problems. To enhance the convergence of MGRIT, we propose the use of consecutive-step coarse-grid operators in MGRIT, rather than the standard rediscretized coarse-grid operators. The consecutive-step coarse-grid operator is defined as the multiplication of several fine-grid operators, which is able to track the advective characteristic more accurately than the standard rediscretized one. Numerical results show that multilevel MGRIT using the proposed operator is more efficient than the one using the standard rediscretized operator when applied to linear advection problems. Moreover, we perform time-parallel computing of the Euler equations and the Navier–Stokes equations by using the proposed method. Spatial coarsening is also considered. Compared with the MGRIT using the standard rediscretization approach, the developed method demonstrates enhanced robustness and efficiency in handling complex flow problems, including cases involving multidimensional shock waves and contact discontinuities.