Paper Info
Title
A high order compact least-squares reconstructed discontinuous Galerkin method for the steady-state compressible flows on hybrid grids.
Abstract
In this paper, a class of new high order reconstructed DG (rDG) methods based on the compact least-squares (CLS) reconstruction [23], [24] is developed for simulating the two dimensional steady-state compressible flows on hybrid grids. The proposed method combines the advantages of the DG discretization with the flexibility of the compact least-squares reconstruction, which exhibits its superior potential in enhancing the level of accuracy and reducing the computational cost compared to the underlying DG methods with respect to the same number of degrees of freedom. To be specific, a third-order compact least-squares rDG(p1p2) method and a fourth-order compact least-squares rDG(p2p3) method are developed and investigated in this work. In this compact least-squares rDG method, the low order degrees of freedom are evolved through the underlying DG(p1) method and DG(p2) method, respectively, while the high order degrees of freedom are reconstructed through the compact least-squares reconstruction, in which the constitutive relations are built by requiring the reconstructed polynomial and its spatial derivatives on the target cell to conserve the cell averages and the corresponding spatial derivatives on the face-neighboring cells. The large sparse linear system resulted by the compact least-squares reconstruction can be solved relatively efficient when it is coupled with the temporal discretization in the steady-state simulations. A number of test cases are presented to assess the performance of the high order compact least-squares rDG methods, which demonstrates their potential to be an alternative approach for the high order numerical simulations of steady-state compressible flows.
Year
DOI
Venue
2018
10.1016/j.jcp.2018.02.012
Journal of Computational Physics
Keywords
Field
DocType
Reconstructed discontinuous Galerkin method,Compact least-squares reconstruction,High order methods,Compressible flows
Least squares,Discontinuous Galerkin method,Compressibility,Applied mathematics,Discretization,Temporal discretization,Polynomial,Linear system,Mathematical analysis,Steady state,Mathematics
Journal
Volume
ISSN
Citations 
362
0021-9991
0
PageRank 
References 
Authors
0.34
14
3
Name
Order
Citations
PageRank
Jian Cheng11327115.72
Fan Zhang222969.82
Tiegang Liu3184.58