相关论文: Nonlinearly Stable Flux Reconstruction High-Order …

This paper develops the high-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamic equations. The schemes are built on the entropy conservative flux and the weighted…

We introduce the Equilibrated Averaging Residual Method (EARM), a unified equilibrated flux-recovery framework for elliptic interface problems that applies to a broad class of finite element discretizations. The method is applicable in both…

Compact Runge-Kutta (cRK) Discontinuous Galerkin (DG) methods, recently introduced in [Q. Chen, Z. Sun, and Y. Xing, SIAM J. Sci. Comput. SIAM J. Sci. Comput., 46: A1327-A1351, 2024], are a variant of RKDG methods for solving hyperbolic…

The shallow water flow model is widely used to describe water flows in rivers, lakes, and coastal areas. Accounting for uncertainty in the corresponding transport-dominated nonlinear PDE models presents theoretical and numerical challenges…

This paper presents a class of novel high-order fully-discrete entropy stable (ES) discontinuous Galerkin (DG) schemes with explicit time discretization. The proposed methodology exploits a critical observation from [4] that the cell…

We present a filter stabilization technique for the mildly compressible Euler equations that relies on a linear or nonlinear indicator function to identify the regions of the domain where artificial viscosity is needed and determine its…

We present a second-order strictly length-preserving and unconditionally energy-stable rotational discrete gradient (Rdg) scheme for the numerical approximation of the Oseen-Frank gradient flows with anisotropic elastic energy functional.…

We present an explicit scheme for a two-dimensional multilayer shallow water model with density stratification, for general meshes and collocated variables. The proposed strategy is based on a regularized model where the transport velocity…

In this article we present a novel staggered semi-implicit hybrid finite-volume/finite-element (FV/FE) method for the resolution of weakly compressible flows in two and three space dimensions. The pressure-based methodology introduced in…

An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional…

For the first time, a general two-parameter family of entropy conservative numerical fluxes for the shallow water equations is developed and investigated. These are adapted to a varying bottom topography in a well-balanced way, i.e.…

We propose an explicit partitioned (loosely coupled) scheme for fluid structure interaction (FSI) problems, specifically designed to achieve high computational efficiency in modern engineering simulations. The FSI problem under…

In this work, we propose an accurate, robust, and stable discretization of the gamma-based compressible multicomponent model by Shyue [J. Comput. Phys., 142 (1998), 208-242] where each component follows a stiffened gas equation of state…

We analyse three time integration schemes for unfitted methods in fluid structure interaction. In Alghorithm 1 we propose a fully discrete monolithic algorithm with P1 P1 stabilized finite elements for the fluid problem; for this alghorithm…

We present a novel combination of numerical techniques to improve the efficiency, accuracy, and robustness of multi-component compressible flow simulations. At the core of our approach is an Entropy-Stable formulation that preserves kinetic…

This study aims to reconstruct the complete flow field from spatially restricted domain data by utilizing an Enhanced Super-Resolution Generative Adversarial Network (ESRGAN) model. The difficulty in flow field reconstruction lies in…

We present the hybridization of flux reconstruction methods for advection-diffusion problems. Hybridization introduces a new variable into the problem so that it can be reduced via static condensation. This allows the solution of implicit…

This article presents a high order conservative flux optimization (CFO) finite element method for the elliptic diffusion equations. The numerical scheme is based on the classical Galerkin finite element method enhanced by a flux…

In this paper, we propose a simple numerical algorithm based on the weak Galerkin (WG) finite element method for a class of fourth-order problems in fluorescence tomography (FT), eliminating the need for stabilizer terms required in…

The robustness and accuracy of marginally resolved discontinuous Galerkin spectral element computations are evaluated for the standard formulation and a kinetic energy conserving split form on complex flow problems of physical and…