LDG2: A variant of the LDG flux formulation for the spectral volume method The local discontinuous Galerkin (LDG) viscous flux formulation was originally developed by Cockburn and Shu for the discontinuous Galerkin setting and later extended to the spectral volume setting by Wang and his collaborators. Unlike the penalty formulations like the interior penalty and the BR2 schemes, the LDG formulation requires no length based penalizing terms and is compact. However, computational results using LDG are dependant of the orientation of the faces especially for unstructured and non uniform grids. This results in lower solution accuracy and stiffer stability constraints as shown by Kannan and Wang. In this paper, we develop a variant of the LDG, which not only retains its attractive features, but also vastly reduces its unsymmetrical nature. This variant (aptly named LDG2), displayed higher accuracy than the LDG approach and has a milder stability constraint than the original LDG formulation. In general, the 1D and the 2D numerical results are very promising and indicate that the approach has a great potential for 3D flow problems.

References in zbMATH (referenced in 14 articles , 1 standard article )

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  1. Felix, I. C.; Okuonghae, R. I.: On the generalisation of Padé approximation approach for the construction of (p)-stable hybrid linear multistep methods (2019)
  2. Quaegebeur, Samuel; Nadarajah, Siva: Stability of energy stable flux reconstruction for the diffusion problem using the interior penalty and bassi and rebay II numerical fluxes for linear triangular elements (2019)
  3. Stipcich, G.; Piller, M.: Unstructured, curved elements for the two-dimensional high order discontinuous control-volume/finite-element method (2015)
  4. Hufford, Casey; Xing, Yulong: Superconvergence of the local discontinuous Galerkin method for the linearized Korteweg-de Vries equation (2014)
  5. Liang, Chunlei; Miyaji, Koji; Zhang, Bin: An efficient correction procedure via reconstruction for simulation of viscous flow on moving and deforming domains (2014)
  6. Williams, D. M.; Jameson, A.: Energy stable flux reconstruction schemes for advection-diffusion problems on tetrahedra (2014)
  7. Castonguay, P.; Vincent, P. E.; Jameson, A.: A new class of high-order energy stable flux reconstruction schemes for triangular elements (2012)
  8. Chen, James; Liang, Chunlei; Lee, James D.: Numerical simulation for unsteady compressible micropolar fluid flow (2012)
  9. Kannan, Ravi; Wang, Zhi Jian: A high order spectral volume solution to the Burgers equation using the Hopf-Cole transformation (2012)
  10. Balakrishnan, Kaushik; Menon, Suresh: Characterization of the mixing layer resulting from the detonation of heterogeneous explosive charges (2011)
  11. Kannan, R.: A high order spectral volume method for elastohydrodynamic lubrication problems: formulation and application of an implicit p-multigrid algorithm for line contact problems (2011)
  12. Kannan, Ravishekar; Wang, Zhi Jian: LDG2: A variant of the LDG flux formulation for the spectral volume method (2011)
  13. Kannan, R.; Wang, Z. J.: Curvature and entropy based wall boundary condition for the high-order spectral volume Euler solver (2011)
  14. Stipcich, G.; Piller, M.; Pivetta, M.; Zovatto, L.: Discontinuous control-volume/finite-element method for advection-diffusion problems (2011)