Related papers: A variable high-order shock-capturing finite diffe…
High-order gas-kinetic scheme (HGKS) has been well-developed in the past years. Abundant numerical tests including hypersonic flow, turbulence, and aeroacoustic problems, have been used to validate its accuracy, efficiency, and robustness.…
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…
In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme for scalar hyperbolic conservation laws in multidimensions. Compared with previous work for linear hyperbolic equations \cite{guo2016transport,…
In this paper, high order semi-implicit well-balanced and asymptotic preserving finite difference WENO schemes are proposed for the shallow water equations with a non-flat bottom topography. We consider the Froude number ranging from O(1)…
Accurate modeling of sea ice dynamics is critical for predicting environmental variables and is important in applications such as navigating ice breaker ships. Research for both modeling and simulating sea ice dynamics is ongoing, with the…
Studies of hadron resonances and their properties are limited by the accuracy and consistency of measured datasets, which can originate from many different experiments. We have used Gaussian Processes (GP) to build interpolated datasets,…
In our previous work [29], we proposed a class of high-order asymptotic preserving (AP) finite difference weighted essentially non-oscillatory (WENO) schemes for solving the shallow water equations (SWEs) with bottom topography and Manning…
The central-upwind weighted essentially non-oscillatory (WENO) scheme introduces the downwind substencil to reconstruct the numerical flux, where the smoothness indicator for the downwind substencil is of critical importance in maintaining…
In this work we aim at developing a new class of high order accurate well-balanced finite difference (FD) Weighted Essentially Non-Oscillatory (WENO) methods for numerical general relativity, which can be applied to any first-order…
In recent years, machine learning has been used to create data-driven solutions to problems for which an algorithmic solution is intractable, as well as fine-tuning existing algorithms. This research applies machine learning to the…
We propose a class of essentially non-oscillatory schemes with adaptive order (ENO-AO) for solving hyperbolic conservation laws. The new schemes select candidate stencils by novel smoothness indicators which are the measurements of the…
The discontinuous Galerkin (DG) finite element method when applied to hyperbolic conservation laws requires the use of shock-capturing limiters in order to suppress unphysical oscillations near large solution gradients. In this work we…
In this paper, a new family of very-high-order TENO schemes with adaptive accuracy order and adaptive dissipation control (TENO-AA) is proposed. The new framework allows for constructing arbitrarily high-order TENO schemes in a unified…
Weighted essentially non-oscillatory (WENO) reconstruction schemes are presented that preserve cylindrical symmetry for radial flows on an equal-angle polar mesh. These new WENO schemes are used with a Lagrangian discontinuous Galerkin (DG)…
In the previous studies, the high-order gas-kinetic schemes (HGKS) have achieved successes for unsteady flows on three-dimensional unstructured meshes. In this paper, to accelerate the rate of convergence for steady flows, the implicit…
In this paper, a simple fifth-order finite difference Hermite WENO (HWENO) scheme combined with limiter is proposed for one- and two- dimensional hyperbolic conservation laws. The fluxes in the governing equation are approximated by the…
We introduce a new numerical strategy to solve a class of oscillatory transport PDE models which is able to captureaccurately the solutions without numerically resolving the high frequency oscillations {\em in both space and time}.Such PDE…
This paper is concerned with generalized polynomial chaos (gPC) approximation for a general system of quasilinear hyperbolic conservation laws with uncertainty. The one-dimensional (1D) hyperbolic system is first symmetrized with the aid of…
In this paper, a modified version of conservative Physics-informed Neural Networks (cPINN for short) is provided to construct the weak solutions of Riemann problem for the hyperbolic scalar conservation laws in non-conservative form. To…
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…