Adaptive remeshing for compressible flow computations
Journal of Computational Physics
Approximate Riemann solvers, parameter vectors, and difference schemes
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
A Cartesian grid finite-volume method for the advection-diffusion equation in irregular geometries
Journal of Computational Physics
Adaptive Galerkin finite element methods for partial differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Grid adaptation for functional outputs: application to two-dimensional inviscid flows
Journal of Computational Physics
Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations
Journal of Computational Physics
Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows
Journal of Computational Physics
Journal of Computational Physics
Adjoint-based h-p adaptive discontinuous Galerkin methods for the 2D compressible Euler equations
Journal of Computational Physics
Error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations
Journal of Computational Physics
Space-time discontinuous Galerkin finite element method for two-fluid flows
Journal of Computational Physics
An Entropy Adjoint Approach to Mesh Refinement
SIAM Journal on Scientific Computing
Journal of Computational Physics
A stable interface element scheme for the p-adaptive lifting collocation penalty formulation
Journal of Computational Physics
An optimization-based framework for anisotropic simplex mesh adaptation
Journal of Computational Physics
Interpolation of two-dimensional curves with Euler spirals
Journal of Computational and Applied Mathematics
PDE-constrained optimization with error estimation and control
Journal of Computational Physics
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This paper presents a mesh adaptation method for higher-order (p1) discontinuous Galerkin (DG) discretizations of the two-dimensional, compressible Navier-Stokes equations. A key feature of this method is a cut-cell meshing technique, in which the triangles are not required to conform to the boundary. This approach permits anisotropic adaptation without the difficulty of constructing meshes that conform to potentially complex geometries. A quadrature technique is proposed for accurately integrating on general cut cells. In addition, an output-based error estimator and adaptive method are presented, appropriately accounting for high-order solution spaces in optimizing local mesh anisotropy. Accuracy on cut-cell meshes is demonstrated by comparing solutions to those on standard, boundary-conforming meshes. Robustness of the cut-cell and adaptation technique is successfully tested for highly anisotropic boundary-layer meshes representative of practical high Re simulations. Furthermore, adaptation results show that, for all test cases considered, p=2 and p=3 discretizations meet desired error tolerances using fewer degrees of freedom than p=1.