相关论文: A mimetic discretization of Westervelt's equation

We introduce a dissipative particle dynamics scheme for the dynamics of non-ideal fluids. Given a free-energy density that determines the thermodynamics of the system, we derive consistent conservative forces. The use of these effective,…

Mathematical descriptions of flow phenomena usually come in the form of partial differential equations. The differential operators used in these equations may have properties such as symmetry, skew-symmetry, positive or negative…

Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional…

A discretization of a continuum theory with constraints or conserved quantities is called mimetic if it mirrors the conserved laws or constraints of the continuum theory at the discrete level. Such discretizations have been found useful in…

A good representation of mesoscopic fluids is required to combine with molecular simulations at larger length and time scales (De Fabritiis {\it et. al}, Phys. Rev. Lett. 97, 134501 (2006)). However, accurate computational models of the…

It is well known that the Lagrangian and Hamiltonian descriptions of field theories are equivalent at the discrete time level when variational integrators are used. Besides the symplectic Hamiltonian structure, many physical systems exhibit…

We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…

We present a new temporal discretization paradigm for developing energy-production-rate preserving numerical approximations to thermodynamically consistent partial differential equation systems, called the supplementary variable method. The…

In this work, we design and analyze semi/fully-discrete virtual element approximations for the time-dependent Navier--Stokes-Cahn--Hilliard equations, modeling the dynamics of two-phase incompressible fluid flows with diffuse interfaces. A…

Diffusion behaviors of heterogeneous materials are of paramount importance in many engineering problems. Numerical models that take into account the internal structure of such materials are robust but computationally very expensive. This…

A conforming finite element scheme with mixed explicit-implicit time discretization for quasi-incompressible Navier-Stokes-Maxwell-Stefan systems in a bounded domain with periodic boundary conditions is presented. The system consists of the…

In contrast to conservative systems, in nonlinear media with gain and loss the dynamics of localized topological structures can exhibit unique features that can be controlled externally. We propose a robust mechanism to perform topological…

We present a finite element discretization of a non-linear diffusion equation used in the field of critical phenomena and, more recently, in the context of Dynamic Density Functional Theory. The discretized equation preserves the structure…

We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…

The hydrodynamics of viscoelastic materials (for example polymer melts and solutions) presents interesting and complex phenomena, for example instabilities and turbulent flow at very low Reynolds numbers due to normal stress effects and the…

On the basis of loop group decompositions (Birkhoff decompositions), we give a discrete version of the nonlinear d'Alembert formula, a method of separation of variables of difference equations, for discrete constant negative Gauss curvature…

In this work, a kernel-based surrogate for integrating Hamiltonian dynamics that is symplectic by construction and tailored to large prediction horizons is proposed. The method learns a scalar potential whose gradient enters a…

We consider the non-isothermal flow of a compressible fluid through pipes. Starting from the full set of Euler equations, we propose a variational characterization of solutions that encodes the conservation of mass, energy, and entropy in a…

The main purpose of this article is to show how symmetry structures in partial differential equations can be preserved in a discrete world and reflected in difference schemes. Three different structure preserving discretizations of the…

The Westervelt equation describes the propagation of pressure waves in continuous nonlinear and, eventually, diffusive media. The classical framework of this equation corresponds to fluid dynamics theory. This work seeks to connect this…