Related papers: A compact high-order gas-kinetic scheme on unstruc…
We develop high-order flux splitting schemes for the one- and two-dimensional Euler equations of gas dynamics. The proposed schemes are high-order extensions of the existing first-order flux splitting schemes introduced in [ E. F. Toro, M.…
We present a novel arbitrary high order accurate central WENO spatial reconstruction procedure (CWENO) for the solution of nonlinear systems of hyperbolic conservation laws on fixed and moving unstructured simplex meshes in two and three…
In recent years, non-equilibrium flows have gained significant attention in aerospace engineering and micro-electro-mechanical systems. The unified gas-kinetic scheme (UGKS) follows the methodology of direct modeling to couple particle…
The unified gas-kinetic scheme (UGKS) is becoming increasingly popular for multiscale simulations in all flow regimes. This paper provides the first analytical study on the stability of the UGKS applied to a linear kinetic model, which is…
High order finite volume schemes for conservation laws are very useful in applications, due to their ability to compute accurate solutions on quite coarse meshes and with very few restrictions on the kind of cells employed in the…
The flow regime of micro flow varies from collisionless regime to hydrodynamic regime according to the Knudsen number. On the kinetic scale, the dynamics of micro flow can be described by the linearized kinetic equation. In the continuum…
Hybrid high-order (HHO) methods are numerical methods characterized by several interesting properties such as local conservativity, geometric flexibility and high-order accuracy. Here, HHO schemes are studied for the space…
Shallow water moment equations are reduced-order models for free-surface flows that allow to represent vertical variations of the velocity profile at the expense of additional evolution equations for a number of additional variables, so…
We develop a high-order kinetic scheme for entropy-based moment models of a one-dimensional linear kinetic equation in slab geometry. High-order spatial reconstructions are achieved using the weighted essentially non-oscillatory (WENO)…
An automatically differentiable, high-order non-oscillatory finite volume shallow water dynamic core has been constructed on a cubed sphere grid. This dynamic core has four advantageous properties: high order accuracy, essential…
This paper introduces an effcient class of adaptive stencil extension reconstruction methods based on a discontinuity feedback factor, addressing the challenges of weak robustness and high computational cost in high-order schemes,…
This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Non-oscillatory…
A third-order weighted essentially non-oscillatory compact least-squares scheme is developed for the finite volume method on structured curvilinear non-uniform grids. The proposed scheme features compact least-squares reconstruction with…
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different…
We propose an unconditionally energy-stable, orthonormality-preserving, component-wise splitting iterative scheme for the Kohn-Sham gradient flow based model in the electronic structure calculation. We first study the scheme discretized in…
This article aims at developing a high order pressure-based solver for the solution of the 3D compressible Navier-Stokes system at all Mach numbers. We propose a cell-centered discretization of the governing equations that splits the fluxes…
Based on the Jacobi polynomial expansion, an arbitrary high-order Discontinuous Galerkin solver for compressible flows on unstructured meshes is proposed in the present work. First, we construct orthogonal polynomials for 2D and 3D…
In order to further enhance the computational efficiency of the implicit unified gas-kinetic scheme (IUGKS, JCP 315 (2016) 16-38) for multi-scale flow simulation, a two-step IUGKS is proposed in this paper. The multiscale solution of the…
We present a novel data-driven approach for enhancing gradient reconstruction in unstructured finite volume methods for hyperbolic conservation laws, specifically for the 2D Euler equations. Our approach extends previous structured-grid…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…