An ALE residual distribution scheme for the unsteady Euler equations over triangular grids with local mesh adaptation. (15th May 2022)

• Record Type: Journal Article
• Authors: Colombo, Stefano; Re, Barbara
• Is Part Of: Computers & fluids. Volume 239(2022)
• Publication Date: 2022-05-15
• Subjects: Unstructured mesh adaptation -- Residual distribution schemes -- Arbitrary Lagrangian–Eulerian (ALE) framework -- Unsteady Euler equations -- Geometric conservation law (GCL); Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2022.105414
• Languages: English
• ISSNs: 0045-7930

Abstract

Abstract: This work presents a novel interpolation-free mesh adaptation technique for the Euler equations within the arbitrary Lagrangian–Eulerian framework. For the spatial discretization, we consider a residual distribution scheme, which provides a pretty simple way to achieve high order accuracy on unstructured grids. Thanks to a special interpretation of the mesh connectivity changes as a series of fictitious continuous deformations, we can enforce by construction the so-called geometric conservation law, which helps to avoid spurious oscillations while solving the governing equations over dynamic domains. This strategy preserves the numerical properties of the underlying, fixed-connectivity scheme, such as conservativeness and stability, as it avoids an explicit interpolation of the solution between different grids. The proposed approach is validated through the two-dimensional simulations of steady and unsteady flow problems over unstructured grids. Highlights: Innovative residual distribution scheme for adaptive triangular grids. Arbitrary Lagrangian–Eulerian formulation used to avoid solution interpolation. Geometric conservation law enforced by construction. Well-suited scheme for unsteady inviscid flow problems with boundary movement.