相关论文: High-order Space-time Flux Reconstruction Methods …
The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage…
In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…
This article presents a high order conservative flux optimization (CFO) finite element method for the elliptic diffusion equations. The numerical scheme is based on the classical Galerkin finite element method enhanced by a flux…
We propose a model order reduction framework for incompressible fluid-structure interaction (FSI) problems based on high-order implicit Runge-Kutta (IRK) methods. We consider separate reduced spaces for fluid velocity, fluid pressure and…
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…
Classical Computational Fluid Dynamics (CFD) of long-time processes with strongly separated time scales is computationally extremely demanding if not impossible. Consequently, the state-of-the-art description of such systems is not capable…
The three-dimensional Time-Resolved Lagrangian Particle Tracking (3D TR-LPT) technique has recently advanced flow diagnostics by providing high spatiotemporal resolution measurements under the Lagrangian framework. To fully exploit its…
The goal of this paper is to develop a high order numerical method based on Kinetic Inviscid Flux (KIF) method and Flux Reconstruction (FR) framework. The KIF aims to find a balance between the excellent merits of Gas-Kinetic Scheme (GKS)…
Time domain simulations of electromagnetic problems are highly valuable in engineering applications, as they allow for the analysis of transient behavior and broadband responses. These simulations utilize time stepping schemes, where each…
We study the long-time error behavior of correction procedure via reconstruction / flux reconstruction (CPR/FR) methods for linear hyperbolic conservation laws. We show that not only the choice of the numerical flux (upwind or central)…
We extend the fourth order, two stage Multi-Derivative Runge Kutta (MDRK) scheme to the Flux Reconstruction (FR) framework by writing both stages in terms of a time averaged flux and then using the approximate Lax-Wendroff procedure to…
This work extends the high-resolution isogeometric analysis approach established for scalar transport equations to the equations of gas dynamics. The group finite element formulation is adopted to obtain an efficient assembly procedure for…
High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the…
In this work, we introduce a new Hybrid High-Order method for the numerical simulation of fracture propagation based on phase-field models. The proposed method supports general meshes made of polygonal/polyhedral elements, which provides…
Hyperbolic conservation laws are conventionally solved by evolving reconstructed floating-point fields, incurring both computational overhead and structural diffusion near discontinuities. Here we introduce the Fast Quantised Numerical…
Floating offshore structures often exhibit low-frequency oscillatory motions in the horizontal plane, with amplitudes in the same order as their characteristic dimensions and larger than the corresponding wave-frequency responses, making…
In this paper, we present a high-order unified gas-kinetic scheme (UGKS) using the weighted essentially non-oscillatory with adaptive-order (WENO-AO) method for spatial reconstruction and the two-stage fourth-order scheme for time…
We develop a $ P $-multigrid solver to simulate locally preconditioned unsteady compressible Navier-Stokes equations at low Mach numbers with implicit high-order methods. Specifically, the high-order flux reconstruction/correction procedure…
We introduce a general framework for enforcing local or global maximum principles in high-order space-time discretizations of a scalar hyperbolic conservation law. We begin with sufficient conditions for a space discretization to be bound…
We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the…