二维Burgers方程非线性多重网格法转移算子效率比较

Efficiency Comparison of Transfer Operators in Nonlinear Multigrid for the Two-Dimensional Burgers Equation

摘要: 本文研究二维无粘Burgers方程稳态求解中非线性多重网格转移算子的计算效率。空间离散过程中采用有限体积法和Rusanov数值通量，时间离散采用伪时间迭代，并比较不同转移算子组合下的收敛表现。数值实验说明了合适的转移算子组合能够明显减少迭代步数和计算时间，其中双线性伴随限制与双线性延拓组合在二阶格式下表现最优。含激波算例进一步表明，高阶转移算子能够加快光滑区的残差衰减，同时保持激波附近的迭代稳定性和数值解质量。

Abstract: This paper investigates the computational efficiency of nonlinear multigrid-transfer operators for the steady-state solution of the two-dimensional inviscid Burgers equation. In the spatial discretization, the finite volume method and the Rusanov numerical flux are employed, while pseudo-time iteration is used for temporal advancement. The convergence performance of different combinations of transfer operators is then compared. Numerical experiments show that an appropriate combination of transfer operators can significantly reduce both the number of iterations and the computational time. In particular, the combination of bilinear-adjoint restriction and bilinear prolongation exhibits the best performance for the second-order scheme. The shock-containing test case further shows that high-order transfer operators can accelerate residual decay in smooth regions while maintaining iterative stability and solution quality near the shock.