A Simplified Boundary Closure for Second- and Third-Order Edge-Based Solvers with Implicit Edge-Based Gradients

In this paper, we introduce a simplified boundary closure for second- and third-order node-centered edge-based discretizations. The main idea is to employ the general accuracy-preserving boundary-flux quadrature formula, separate the flux contributions involving neighbor nodes, incorporate them into an interior edge loop, and then account for the remaining contributions in a loop over boundary nodes. This new approach effectively reduces the computational operations and eliminates the need to access neighbors in a boundary closure loop. Numerical results show that the approach can enhance iterative convergence and reduce computational time for second- and third-order edge-based solvers.