Journal of Computational Physics
High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation
Journal of Computational Physics
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Aspects of discontinuous Galerkin methods for hyperbolic conservation laws
Finite Elements in Analysis and Design - Robert J. Melosh medal competition
Nodal high-order methods on unstructured grids
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Spectral difference method for unstructured grids I: basic formulation
Journal of Computational Physics
Short Note: On the connection between the spectral volume and the spectral difference method
Journal of Computational Physics
A Study of Viscous Flux Formulations for a p-Multigrid Spectral Volume Navier Stokes Solver
Journal of Scientific Computing
A stable interface element scheme for the p-adaptive lifting collocation penalty formulation
Journal of Computational Physics
Journal of Computational Physics
A New Class of High-Order Energy Stable Flux Reconstruction Schemes for Triangular Elements
Journal of Scientific Computing
Journal of Scientific Computing
Journal of Computational Physics
Hi-index | 31.45 |
This paper presents a polynomial-adaptive lifting collocation penalty (LCP) formulation for the compressible Navier-Stokes equations. The LCP formulation is a high-order nodal scheme in differential form. This format, although computationally efficient, complicates the treatment of non-uniform polynomial approximations. In Cagnone and Nadarajah (2012) [9], we proposed to circumvent this difficulty by employing specially designed elements inserted at the interface where the interpolation degree varies. In the present study we examine the applicability of this approach to the discretization of the Navier-Stokes equations, with focus put on the treatment of the viscous fluxes. The stability of the scheme is analyzed with the scalar diffusion equation and the merits of the approach are demonstrated with various p-adaptive simulations.