相关论文: Nonlinearly Stable Flux Reconstruction High-Order …

Because of their capability to preserve steady-states, well-balanced schemes for Shallow Water equations are becoming popular. Among them, the hydrostatic reconstruction proposed in Audusse et al. (2004), coupled with a positive numerical…

Kinetic schemes for compressible flow of gases are constructed by exploiting the connection between Boltzmann equation and the Navier-Stokes equations. This connection allows us to construct a flux splitting for the Navier-Stokes equations…

Friedrichs' systems (FS) are symmetric positive linear systems of first-order partial differential equations (PDEs), which provide a unified framework for describing various elliptic, parabolic and hyperbolic semi-linear PDEs such as the…

We introduce a novel positivity-preserving, parameter-free numerical stabilisation approach for high-order discontinuous spectral element approximations of compressible multi-species flows. The underlying stabilisation method is the…

We present a nonlinear stabilized Lagrange-Galerkin scheme for the Oseen-type Peterlin viscoelastic model. Our scheme is a combination of the method of characteristics and Brezzi-Pitk\"aranta's stabilization method for the conforming linear…

This paper develops the high-order entropy stable (ES) finite difference schemes for multi-dimensional compressible Euler equations with the van der Waals equation of state (EOS) on adaptive moving meshes. Semi-discrete schemes are first…

We propose an entropy-stable conservative flux form neural network (CFN) that integrates classical numerical conservation laws into a data-driven framework using the entropy-stable, second-order, and non-oscillatory Kurganov-Tadmor (KT)…

A well-designed numerical method for the shallow water equations (SWE) should ensure well-balancedness, nonnegativity of water heights, and entropy stability. For a continuous finite element discretization of a nonlinear hyperbolic system…

The evolve-filter (EF) model is a filter-based numerical stabilization for under-resolved convection-dominated flows. EF is a simple, modular, and effective strategy for both full-order models (FOMs) and reduced-order models (ROMs). It is…

The correction procedure via reconstruction (CPR, also known as flux reconstruction) is a framework of high order semidiscretisations used for the numerical solution of hyperbolic conservation laws. Using a reformulation of these schemes…

In this paper we present two unconditionally energy stable finite difference schemes for the Modified Phase Field Crystal (MPFC) equation, a sixth-order nonlinear damped wave equation, of which the purely parabolic Phase Field Crystal (PFC)…

We develop a novel and efficient discontinuous Galerkin spectral element method (DG-SEM) for the spherical rotating shallow water equations in vector invariant form. We prove that the DG-SEM is energy stable, and discretely conserves mass,…

Lax-Wendroff Flux Reconstruction (LWFR) is a single-stage, high order, quadrature free method for solving hyperbolic conservation laws. We develop a subcell based limiter by blending LWFR with a lower order scheme, either first order finite…

Logarithmic conformation reformulations for viscoelastic constitutive laws have alleviated the high Weissenberg number problem, and the exploration of highly elastic flows became possible. However, stabilized formulations for logarithmic…

Modeling microstructural evolution at large strains requires mechanical formulations that remain thermodynamically consistent while capturing significant lattice rotations and transformation-induced stresses. However, most existing…

A Skeleton-stabilized ImmersoGeometric Analysis technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed formulation fits within the framework of the finite cell method, where essential…

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…

In this paper, a robustness-enhanced reconstruction for the high-order finite volume scheme is constructed on the 2-D structured mesh, and both the high-order gas-kinetic scheme(GKS) and the Lax-Friedrichs(L-F) flux solver are considered to…

In this paper, we develop a new mass conservative numerical scheme for the simulations of a class of fluid-structure interaction problems. We will use the immersed boundary method to model the fluid-structure interaction, while the fluid…

In order to prevent velocity, pressure, and temperature spikes at material discontinuities occurring when the interface-capturing schemes inconsistently simulate compressible multi-material flows(when the specific heats ratio is…