High-Order ENO Schemes for Unstructured Meshes Based on Least-Squares Reconstruction

This article is part of an ongoing effort to develop high-order schemes for unstructured meshes to the point where meaningful information can be obtained about the trade-offs involved in using spatial discretizations of higher than second-order accuracy on unstructured meshes. This article describes a high-order accurate ENO reconstruction scheme, called DD-L 2 -ENO, for use with vertex-centered upwind flow solution algorithms on unstructured meshes. The solution of conservation equations in this context can be broken naturally into three phases: 1. Solution reconstruction, in which a polynomial approximation of the solution is obtained in each control volume. 2. Flux integration around each control volume, using an appropriate flux function and a quadrature rule with accuracy commensurate with that of the reconstruction. 3. Time evolution, which may be implicit, explicit, multigrid, or some hybrid. This article focuses primarily on solution reconstruction. A new high-order ENO reconstructio