相关论文: A space-time framework for periodic flows with app…

This study proposes an algorithm for modeling compressible flows in spherical shells in nearly incompressible and weakly compressible regimes based on an implicit direction splitting approach. The method retains theoretically expected…

We present an novel algorithm for tracking massless solid particles in a divergence-free velocity field that is only available at discrete points in space and time such as those arising from a direct numerical simulation of Navier-Stokes.…

Time-evolving perforated domains arise in many engineering and geoscientific applications, including reactive transport, particle deposition, and structural degradation in porous media. Accurately capturing the macroscopic behavior of such…

The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…

We investigate effective equations governing the volume expansion of spatially averaged portions of inhomogeneous cosmologies in spacetimes filled with an arbitrary fluid. This work is a follow-up to previous studies focused on irrotational…

The simulation of large open water surface is challenging using a uniform volumetric discretization of the Navier-Stokes equations. Simulating water splashes near moving objects, which height field methods for water waves cannot capture,…

We show that an attempt to compute numerically a viscous flow in a domain with a piece-wise smooth boundary by straightforwardly applying well-tested numerical algorithms (and numerical codes based on their use, such as COMSOL Multiphysics)…

A spacetime outlook on Computational Fluid Dynamics is advocated: models in fluid mechanics often have the spacetime correlation property, which should be inherited and preserved in the corresponding numerical algorithms. Starting from the…

In the previous work, Zhang et al. proposed a multi-resolution smoothed particle hydrodynamics (SPH) method for fluid-structure interactions (FSI) with achieving an optimized computational efficiency meanwhile maintaining good numerical…

We consider convection-diffusion problems in time-dependent domains and present a space-time finite element method based on quadrature in time which is simple to implement and avoids remeshing procedures as the domain is moving. The…

Advective transport of scalar quantities through surfaces is of fundamental importance in many scientific applications. From the Eulerian perspective of the surface it can be quantified by the well-known integral of the flux density. The…

A numerical method is developed for solving a system of partial differential equations modeling the flow of a nematic liquid crystal fluid with stretching effect, which takes into account the geometrical shape of its molecules. This system…

Optimal-order uniform-in-time $H^1$-norm error estimates are given for semi- and full discretizations of mean curvature flow of surfaces in arbitrarily high codimension. The proposed and studied numerical method is based on a parabolic…

In this paper, a second-order accurate method was developed for calculating fluid flows in complex geometries. This method uses cut-Cartesian cell mesh in finite volume framework. Calculus is employed to relate fluxes and gradients along…

This letter presents a new approach using the cosmic peculiar velocity field to characterize the morphology and size of large scale structures in the local Universe. The algorithm developed uses the three-dimensional peculiar velocity field…

Let $M$ be a manifold equipped (locally) with a pair of complementary foliations. In Catuogno, da Silva and Ruffino (Stoch. Dyn. 2013), it is shown that, up to a stopping time $\tau$, a stochastic flow of local diffeomorphisms $\varphi_t$…

We define notions of differentiability for maps from and to the space of persistence barcodes. Inspired by the theory of diffeological spaces, the proposed framework uses lifts to the space of ordered barcodes, from which derivatives can be…

We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its…

We propose and analyze volume-preserving parametric finite element methods for surface diffusion, conserved mean curvature flow and an intermediate evolution law in an axisymmetric setting. The weak formulations are presented in terms of…

Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose,…