Multidimensional Fifth-Order Compact Reconstruction

• The paper introduces a multidimensional fifth-order compact reconstruction that combines cell averages with derivatives to achieve high-order accuracy in gas-kinetic schemes.
• The method enhances physical and numerical consistency by aligning reconstruction with the gas evolution’s local domain of dependence, reducing numerical dissipation.
• Its effectiveness is validated in turbulence simulations such as the Taylor-Green vortex and turbulent channel flows, demonstrating improved resolution of multi-scale structures.

to=arxiv_search.search ＿欧美json {"^^^^^^^^2query2 OR \2^^^^^^^^"High-order Gas-kinetic Schemes with Non-compact and Compact Reconstruction for Implicit Large Eddy Simulation\"", "max_results": 5, "sort_by": "relevance"} to=arxiv_search.search েউjson {"^^^^^^^^2query2 GKS\" HWENO gas-kinetic scheme reconstruction", "max_results": ^^^^2(Zhao et al., 2022) OR \2query2^^^^, "sort_by": "relevance"} Multidimensional fifth-order compact reconstruction, in the setting of the high-order gas-kinetic scheme (HGKS), is a reconstruction strategy for obtaining the macroscopic states required at cell interfaces when the flux is generated by a time-evolving BGK solution rather than by a Riemann solver. In the formulation studied for implicit large eddy simulation (ILES), the method is multidimensional in the sense that it is applied in three dimensions through a direction-by-direction procedure: the normal direction at a cell interface uses 5th-order compact Hermite WENO reconstruction, while the tangential directions use 5th-order linear reconstruction. Its defining feature is that it combines cell averages with cell-averaged derivatives, thereby achieving 5th-order accuracy with a smaller stencil and with what the paper describes as consistent physical and numerical domains of dependence (&&&^^^^2query2^^^^&&&).

^^^^2(Zhao et al., 2022) OR \2^^^^. Position within high-order gas-kinetic schemes

The reconstruction problem in HGKS is shaped by the structure of the gas-kinetic flux itself. In GKS, the interface flux is not supplied by a Riemann solver; instead, it is obtained from a time-dependent solution of the BGK equation that depends on reconstructed left and right states and their gradients. The reconstruction stage therefore supplies the interface macroscopic data needed for gas evolution, and the quality of that reconstruction directly affects dissipation, resolution, and turbulence fidelity (&&&^^^^2query2^^^^&&&).

The study places multidimensional fifth-order compact reconstruction alongside high-order non-compact reconstruction in the same HGKS framework. The stated objective is to validate both higher-order non-compact reconstruction and compact reconstruction in turbulence simulation, with particular emphasis on ILES in the three-dimensional Taylor-Green vortex problem and turbulent channel flows. Within this comparison, the compact method is not presented merely as a lower-cost approximation to a wider stencil method; it is presented as a reconstruction whose locality is aligned with the physical modeling used by the gas-kinetic evolution (&&&^^^^2query2^^^^&&&).

This alignment is central to the paper’s interpretation of compactness. The compact reconstruction is described as using a smaller stencil plus derivative information, whereas the non-compact reconstruction uses a wider set of neighboring cell averages. This suggests that, in HGKS, compactness is not only a geometrical property of the stencil but also a structural property of how interface information is generated and recycled through cell-averaged derivatives.

2. Motivation for compact reconstruction

The paper gives two explicit motivations for considering compact reconstruction rather than relying solely on non-compact high-order reconstruction. The first is accuracy and dissipation control for ILES. The study states that increasing reconstruction order reduces numerical dissipation, and that compact reconstruction can improve resolution even at lower order. Because the target applications are turbulent flows with multi-scale content, excess numerical dissipation is treated as a primary limitation of lower-order or less effective reconstructions (&&&^^^^2query2^^^^&&&).

The second motivation is stencil efficiency and physical consistency. The compact GKS is described as being able to achieve higher-order accuracy with the same stencils and as generally using fewer cells than the non-compact version for a comparable order. More specifically, the paper emphasizes that compact reconstruction has consistent physical and numerical domains of dependence. In the language of the study, this means that the method does not employ additional information from cells that have no direct physical connection with the targeted cell (&&&^^^^2query2^^^^&&&).

This distinction is particularly significant in turbulence simulation. The paper concludes that the compact GKS shows favorable performance in resolving multi-scale structures. A plausible implication is that the method’s reduced stencil width is not treated only as a computational convenience; it is linked to the preservation of small-scale structure through a less dissipative and more local interface construction.