Related papers: Data-Driven Adaptive Gradient Recovery for Unstruc…
Non-orthogonality errors in unstructured Finite Volume methods for simulating incompressible two-phase flows may break the force-balanced discretization. We show that applying the same explicit non-orthogonality correction for all gradient…
Data reconstruction attacks on trained neural networks aim to recover the data on which the network has been trained and pose a significant threat to privacy, especially if the training dataset contains sensitive information. Here, we…
This paper introduces a novel method for the efficient second-order accurate computation of normal fields from volume fractions on unstructured polyhedral meshes. Locally, i.e. in each mesh cell, an averaged normal is reconstructed by…
We formulate a data-driven, physics-constrained closure method for coarse-scale numerical simulations of turbulent fluid flows. Our approach involves a closure scheme that is non-local both in space and time, i.e. the closure terms are…
In this paper we extend the recently developed third-order limiter function $H_{3\text{L}}^{(c)}$ [J. Sci. Comput., (2016), 68(2), pp.~624--652] to make it applicable for more elaborate test cases in the context of finite volume schemes.…
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…
The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…
In this paper, the compact gas-kinetic scheme for compressible flow is extended to hybrid unstructured mesh. Based on both cell-averaged flow variables and their gradients updated from time accurate gas evolution model at cell interfaces, a…
A second-order face-centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to…
In this paper, we develop bound-preserving (BP) finite-volume schemes for hyperbolic conservation laws on adaptive moving meshes. For scalar conservative laws, we rewrite the conventional high-order discretization as a convex combination of…
Gradient-based iterative optimization methods are the workhorse of modern machine learning. They crucially rely on careful tuning of parameters like learning rate and momentum. However, one typically sets them using heuristic approaches…
This is the second paper on the study of gradient recovery for elliptic interface problem. In our previous work [H. Guo and X. Yang, 2016, arXiv:1607.05898], we developed gradient recovery finite element method based on body-fitted mesh. In…
High-fidelity simulation of complex physical systems is exorbitantly expensive and inaccessible across spatiotemporal scales. Recently, there has been an increasing interest in leveraging deep learning to augment scientific data based on…
This paper presents a data-driven framework for learning optimal second-order total variation diminishing (TVD) flux limiters via differentiable simulations. In our fully differentiable finite volume solvers, the limiter functions are…
We discuss the efficient implementation of a high-performance second-order collocation-type finite-element scheme for solving the compressible Euler equations of gas dynamics on unstructured meshes. The solver is based on the convex…
In the present work, a high order finite element type residual distribution scheme is designed in the framework of multidimensional compressible Euler equations of gas dynamics. The strengths of the proposed approximation rely on the…
Unstructured grid data are essential for modelling complex geometries and dynamics in computational physics. Yet, their inherent irregularity presents significant challenges for conventional machine learning (ML) techniques. This paper…
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…
High order reconstruction in the finite volume (FV) approach is achieved by a more fundamental form of the fifth order WENO reconstruction in the framework of orthogonally-curvilinear coordinates, for solving the hyperbolic conservation…
Wavelet-based grid adaptation methods use multiresolution analysis for error estimation, offering a mathematically rigorous approach to adaptive grid refinement when solving Partial Differential Equations (PDEs). However, applying these…