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Direct reconstruction method for discontinuous Galerkin methods on higher-order mixed-curved meshes I. Volume integration.
- Source :
-
Journal of Computational Physics . Oct2019, Vol. 395, p223-246. 24p. - Publication Year :
- 2019
-
Abstract
- This work deals with the development of the direct reconstruction method (DRM) and its application to the volume integration of the discontinuous Galerkin (DG) method on multi-dimensional high-order mixed-curved meshes. The conventional quadrature-based DG methods require the humongous computational cost on high-order curved elements due to their non-linear shape functions. To overcome this issue, the flux function is directly reconstructed in the physical domain using nodal polynomials on a target space in a quadrature-free manner. Regarding the target space and distribution of the nodal points, DRM has two variations: the brute force points (BFP) and shape function points (SFP) methods. In both methods, one nodal point corresponds to one nodal basis function of the target space. The DRM-BFP method uses a set of points that empirically minimizes a condition number of the generalized Vandermonde matrix. In the DRM-SFP method, the conventional nodal points are used to span an enlarged target space of the flux function. It requires a larger number of reconstruction points than DRM-BFP but offers easy extendability to the higher-degree polynomial space and a better de-aliasing effect. A robust way to compute orthonormal polynomials is provided to achieve lower round-off errors. The proposed methods are validated by the 2-D/3-D Navier-Stokes equations on high-order mixed-curved meshes. The numerical results confirm that the DRM volume integration greatly reduces the computational cost and memory overhead of the conventional quadrature-based DG methods on high-order curved meshes while maintaining an optimal order-of-accuracy as well as resolving the flow physics accurately. • As a quadrature-free method, the DRM framework is proposed and applied to the volume integration of DG methods for the Navier-Stokes equations. • According to the target space and interpolation nodes, DRM-BFP and DRM-SFP are developed on multi-dimensional higher-order mixed-curved mesh. • Through numerical analyses and computations, efficiency and accuracy of DRM are extensively validated on higher-order mixed curved mesh. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GALERKIN methods
*INTERPOLATION spaces
*NUMERICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 00219991
- Volume :
- 395
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Physics
- Publication Type :
- Academic Journal
- Accession number :
- 137973559
- Full Text :
- https://doi.org/10.1016/j.jcp.2019.06.015