Related papers: A compact high-order gas-kinetic scheme on unstruc…
In this paper, a unified framework for particulate two-phase flow will be presented with a wide range of solid-particle concentration from dilute to dense limit. The two phase flow is simulated by two coupled flow solvers, i.e., the…
In this paper, the discrete unified gas kinetic scheme (DUGKS) with an improved microflux across the cell interface for the conservative Allen-Cahn equation (CACE) is proposed. In the context of DUGKS, the recovered kinetic equation from…
A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…
When constructing high-order schemes for solving hyperbolic conservation laws, the corresponding high-order reconstructions are commonly performed in characteristic spaces to eliminate spurious oscillations as much as possible. For…
In this work, third-order semi-implicit schemes on staggered meshes for the shallow water and Saint-Venant-Exner systems are presented. They are based on a third-order extension of the technique introduced in Cassulli \& Cheng [1]. The…
We develop a two-dimensional high-order numerical scheme that exactly preserves and captures the moving steady states of the shallow water equations with topography or Manning friction. The high-order accuracy relies on a suitable…
We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…
The high-order numerical solution of the non-linear shallow water equations (and of hyperbolic systems in general) is susceptible to unphysical Gibbs oscillations that form in the proximity of strong gradients. The solution to this problem…
We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together…
In this paper, we consider two distinct challenges in the resolution of nonsmooth stochastic optimization. Of these, the first pertains to the pronounced dependence of dimension in Gaussian smoothing-enabled zeroth-order schemes, impeding…
Presence of a high-dimensional stochastic parameter space with discontinuities poses major computational challenges in analyzing and quantifying the effects of the uncertainties in a physical system. In this paper, we propose a stochastic…
The general synthetic iteration scheme (GSIS) is extended to find the steady-state solution of nonlinear gas kinetic equation, removing the long-standing problems of slow convergence and requirement of ultra-fine grids in near-continuum…
The shock instability problem commonly arises in flow simulations involving strong shocks, particularly when employing high-order schemes, limiting their applications in hypersonic flow simulations. This study focuses on exploring the…
Numerical schemes used for the integration of complex flow simulations should provide accurate solutions for the long time integrations these flows require. To this end, the performance of various high-order accurate numerical schemes is…
A fully implicit high-order preconditioned flux reconstruction/correction procedure via reconstruction (FR/CPR) method is developed to solve the compressible Navier-Stokes equations at low Mach numbers. A dual-time stepping approach with…
Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems…
The discrete unified gas kinetic scheme (DUGKS) is a finite-volume scheme with discretization of particle velocity space, which combines the advantages of both lattice Boltzmann equation (LBE) method and unified gas kinetic scheme (UGKS)…
Accurate aerodynamic and aerothermodynamic predictions are crucial for numerous hypersonic applications. This paper proposes a gas-kinetic scheme (GKS) coupled with a two-temperature kinetic model, which distinguishes between the…
We present an improved high-order weighted compact high resolution (WCHR) scheme that extends the idea of weighted compact nonlinear schemes (WCNS's) using nonlinear interpolations in conjunction with compact finite difference schemes for…
3D Gaussian Splatting (3DGS) has become a state-of-the-art framework for real-time, high-fidelity novel view synthesis. However, its substantial storage requirements and inherently unstructured representation pose challenges for deployment…