A Discontinuous Galerkin ALE Method for Compressible Viscous Flows in Moving Domains

✍ Scribed by I Lomtev; R.M Kirby; G.E Karniadakis

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 382 KB
• Volume: 155
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1999.6331

✦ Synopsis

We present a matrix-free discontinuous Galerkin method for simulating compressible viscous flows in two-and three-dimensional moving domains. To this end, we solve the Navier-Stokes equations in an arbitrary Lagrangian Eulerian (ALE) framework. Spatial discretization is based on standard structured and unstructured grids but using an orthogonal hierarchical spectral basis. The method is third-order accurate in time and converges exponentially fast in space for smooth solutions. A novelty of the method is the use of a force-directed algorithm from graph theory that requires no matrix inversion to efficiently update the grid while minimizing distortions. We present several simulations using the new method, including validation with published results from a pitching airfoil, and new results for flow past a three-dimensional wing subject to large flapping insect-like motion.