相关论文: Defect-Deferred Correction Method Based on a Subgr…

We propose first-order pressure-correction scheme for the incompressible Navier-Stokes equations, incorporating the recently developed the Dynamically Regularized Lagrange Multiplier (DRLM) methods. The resulting algorithms are fully…

Anomaly Detection (AD), as a critical problem, has been widely discussed. In this paper, we specialize in one specific problem, Visual Defect Detection (VDD), in many industrial applications. And in practice, defect image samples are very…

While many diffusion models have achieved impressive results in real-world video super-resolution (Real-VSR) by generating rich and realistic details, their reliance on multi-step sampling leads to slow inference. One-step networks like…

We propose an implicit Discontinuous Galerkin (DG) discretization for incompressible two-phase flows using an artificial compressibility formulation. The conservative level set (CLS) method is employed in combination with a reinitialization…

The random forced Navier-Stokes equation can be obtained as a variational problem of a proper action. By virtue of incompressibility, the integration over transverse components of the fields allows to cast the action in the form of a large…

An adaptation of the arbitrary high order ADER-DG numerical method with local DG predictor for solving the IVP for a first-order non-linear ODE system is proposed. The proposed numerical method is a completely one-step ODE solver with…

A high-order Flux reconstruction implementation of the hyperbolic formulation for the incompressible Navier-Stokes equation is presented. The governing equations employ Chorin's classical artificial compressibility (AC) formulation cast in…

We propose an algorithm for low Mach number reacting flows subjected to electric field that includes the chemical production and transport of charged species. This work is an extension of a multi-implicit spectral deferred correction…

Navier-Stokes equations are significant partial differential equations that describe the motion of fluids such as liquids and air. Due to the importance of Navier-Stokes equations, the development on efficient numerical schemes is important…

Improved local numerical solution for the ADER-DG numerical method with a local DG predictor for solving the initial value problem for a first-order ODE system is proposed. The improved local numerical solution demonstrates convergence…

This paper concerns a posteriori error analysis for the streamline diffusion (SD) finite element method for the one and one-half dimensional relativistic Vlasov-Maxwell system. The SD scheme yields a weak formulation, that corresponds to an…

We address the solution of the distributed control problem for the steady, incompressible Navier--Stokes equations. We propose an inexact Newton linearization of the optimality conditions. Upon discretization by a finite element scheme, we…

The simulation of fluid flow problems, specifically incompressible flows governed by the Navier-Stokes equations (NSE), holds fundamental significance in a range of scientific and engineering applications. Traditional numerical methods…

In this paper we introduce a novel Neural Networks-based approach for approximating solutions to the (2D) incompressible Navier--Stokes equations, which is an extension of so called Deep Random Vortex Methods (DRVM), that does not require…

In this paper, the convergence of an algorithm for recovering the unknown kinematic viscosity of a two-dimensional incompressible, viscous fluid is studied. The algorithm of interest is a recursive feedback control-based algorithm that…

In this paper we propose a new spatially high order accurate semi-implicit discontinuous Galerkin (DG) method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured curved meshes. While the…

We introduce new adaptive artificial anti-diffusion (AAAD) methods for one- and two-dimensional hyperbolic systems of conservation laws. The key idea is to reduce the amount of numerical dissipation present in a given numerical method by…

In this study, we provide error estimates and stability analysis of deep learning techniques for certain partial differential equations including the incompressible Navier-Stokes equations. In particular, we obtain explicit error estimates…

The Navier-Stokes-Maxwell-Stefan system describes the dynamics of an incompressible gaseous mixture in isothermal condition. In this paper we set up an artificial compressibility type approximation. In particular we focus on the existence…

The selective frequency damping (SFD) method is an alternative to classical Newton's method to obtain unstable steady-state solutions of dynamical systems. However this method has two main limitations: it does not converge for arbitrary…