相关论文: Nonlinearly Stable Flux Reconstruction High-Order …
Provably stable flux reconstruction (FR) schemes are derived for partial differential equations cast in curvilinear coordinates. Specifically, energy stable flux reconstruction (ESFR) schemes are considered as they allow for design…
The flux reconstruction (FR) method has gained popularity within the research community. The approach has been demonstrated to recover high-order methods such as the discontinuous Galerkin (DG) method. Stability analyses have been conducted…
Provable nonlinear stability bounds the discrete approximation and ensures that the discretization does not diverge. For high-order methods, discrete nonlinear stability and entropy stability, have been successfully implemented for…
Energy stable flux reconstruction (ESFR) is a high-order numerical method used for solving partial differential equations in computational fluid dynamics. This method is designed to preserve the energy stability of the underlying partial…
The energy stable flux reconstruction (ESFR) method provides an efficient and flexible framework to devise high-order linearly stable numerical schemes which can achieve high levels of accuracy on unstructured grids. While superconvergent…
A fully-discrete, nonlinearly-stable flux reconstruction (FD-NSFR) scheme is developed, which ensures robustness through entropy stability in both space and time for high-order flux reconstruction schemes. We extend the entropy-stable flux…
The energy stable flux reconstruction (ESFR) method encompasses an infinite family of high-order, linearly stable schemes and thus provides a flex- ible and efficient framework for achieving high levels of accuracy on unstruc- tured grids.…
We present a high-order space-time discretization equipped with fully-discrete entropy stability properties for general choices of volume and surface quadrature rules. The formulation uses flux reconstruction (FR) in the spatial dimension…
In the case of hyperbolic conservation laws, high-order methods, such as the classical DG method, experience the phenomenon of unwanted high-frequency oscillations in the vicinity of a shock. Shock-capturing methods such as artificial…
Recovering some prominent high-order approaches such as the discontinuous Galerkin (DG) or the spectral difference (SD) methods, the flux reconstruction (FR) approach has been adopted by many individuals in the research community and is now…
Nonlinearly stable flux reconstruction (NSFR) combines the key properties of provable nonlinear stability with the increased time step from energy-stable flux reconstruction. The NSFR scheme has been successfully applied to unsteady…
In this work, we develop a new hydrostatic reconstruction procedure to construct well-balanced schemes for one and multilayer shallow water flows, including wetting and drying. Initially, we derive the method for a path-conservative finite…
We present an extended range of stable flux reconstruction (FR) methods on triangles through the development and application of the summation-by-parts framework in two-dimensions. This extended range of stable schemes is then shown to…
A stability analysis is performed on high-order schemes formulated using the Flux Reconstruction (FR) approach. The one-dimensional advection model equation is used for the assessment of the stability region of these schemes when coupled…
Fisher and Carpenter (\textit{High-order entropy stable finite difference schemes for non-linear conservation laws: Finite domains, Journal of Computational Physics, 252:518--557, 2013}) found a remarkable equivalence of general diagonal…
The flux reconstruction (FR) approach offers a flexible framework for describing a range of high-order numerical schemes; including nodal discontinuous Galerkin and spectral difference schemes. This is accomplished through the use of…
The performance of the nonlinearly stable flux reconstruction (NSFR) schemes for resolving subsonic viscous turbulent free-shear flows is investigated. The schemes are extensively verified for the direct numerical simulation (DNS) of the…
The study of uncertainty propagation poses a great challenge to design numerical solvers with high fidelity. Based on the stochastic Galerkin formulation, this paper addresses the idea and implementation of the first flux reconstruction…
High-order nodal space-time flux reconstruction (STFR) methods have been developed to solve hyperbolic conservation laws on curvilinear moving grids. Unlike the method-of-lines approach for moving domain simulation, the grid velocity is…
The focus of the present research is on the analysis of local energy stability of high-order (including split-form) summation-by-parts methods, with e.g. two-point entropy-conserving fluxes, approximating non-linear conservation laws. Our…