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Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been…
We present a stable spectral vanishing viscosity for discontinuous Galerkin schemes, with applications to turbulent and supersonic flows. The idea behind the SVV is to spatially filter the dissipative fluxes, such that it concentrates in…
We consider finite-volume schemes for linear hyperbolic systems with constant coefficients on unstructured meshes. Under the stability assumption, they exhibit the convergence rate between $p$ and $p+1$ where $p$ is the order of the…
In this paper, a compact high-order gas-kinetic scheme (GKS) with spectral resolution will be presented and used in the simulation of acoustic and shock waves. For accurate simulation, the numerical scheme is required to have excellent…
A scheme to reduce translational noninvariant quasi-one-dimensional wave guides into singly or multiply connected one-dimensional (1D) lines is proposed. It is meant to simplify the analysis of wave guides, with the low-energy properties of…
We proposed a piecewise quadratic reconstruction method in multiple dimensions, which is in an integrated style, for finite volume schemes to scalar conservation laws. This integrated quadratic reconstruction is parameter-free and…
In this paper, we study the Mach reflection phenomenon in inviscid flows using a higher order discontinuous Galerkin method and overset grids. We use the shock capturing procedure proposed in Siva Prasad Kochi et al. using overset grids to…
The outcomes of projective measurements on a quantum many-body system in a chosen basis are inherently probabilistic. The Shannon entropy of this probability distribution (the "diagonal entropy") often reveals universal features, such as…
An incremental-stencil WENO reconstruction method, which uses low-order candidate stencils with incrementally increasing width, is proposed for finite-volume simulation of compressible two-phase flow with the quasi-conservative interface…
Many numerical schemes for hyperbolic systems require a piecewise polynomial reconstruction of the cell averaged values, and to simulate perturbed steady states accurately we require a so called 'well balanced' reconstruction scheme. For…
This article aims at presenting a new local subcell monolithic Discontinuous-Galerkin/Finite-Volume (DG/FV) convex property preserving scheme solving system of conservation laws on 2D unstructured grids. This is known that DG method needs…
A fully coupled implicit finite-volume algorithm for incompressible viscoelastic interfacial flows is proposed, whereby the viscoelasticity of the flow is described by an upper-convected Maxwell constitutive model, including limited…
A high order finite difference method is proposed for unstructured meshes to simulate compressible inviscid/viscous flows with/without discontinuities. In this method, based on the strong form equation, the divergence of the flux on each…
In this paper we develop a non-diffusive neural network (NDNN) algorithm for accurately solving weak solutions to hyperbolic conservation laws. The principle is to construct these weak solutions by computing smooth local solutions in…
The need for an efficient method of integration of a dense normal field is inspired by several computer vision tasks, such as shape-from-shading, photometric stereo, deflectometry, etc. Inspired by edge-preserving methods from image…
Predicting the mechanics of large structural networks, such as beam-based architected materials, requires a multiscale computational strategy that preserves information about the discrete structure while being applicable to large assemblies…
This work primarily focuses on the study of three gradient reconstruction techniques applied to the calculation of viscous terms in a cell-centered, finite volume formulation for general unstructured grids. The work also addresses different…
This paper is concerned with the construction of high order schemes on irregular grids for balance laws, including a discussion of an a-posteriori error indicator based on the numerical entropy production. We also impose well-balancing on…
3D volumetric reconstruction from incomplete or noisy measurements is a fundamental problem in medical imaging and computational tomography. Deep image prior (DIP)-based methods have recently shown strong capability for solving inverse…
Tensor hypercontraction provides an attractive four-center two-electron repulsion integral format that can lower the scaling of many electronic structure methods while only requiring O(N^2) memory. However, in its grid-based least-squares…