Related papers: Convecting reference frames and invariant numerica…
Models of turbulent flows require the resolution of a vast range of scales, from large eddies to small-scale features directly associated with dissipation. As the required resolution is not within reach of large scale numerical simulations,…
We perform numerical analysis of a nonlinear gradient flow, which can be regarded as a parabolic minimal surface problem or a regularised total variation flow, using the gradient discretisation method (GDM). GDM is a unified convergence…
This papers shows the convergence of optimal control problems where the constraint function is discretised by a particle method. In particular, we investigate the viscous Burgers equation in the whole space $\mathbb R$ by using…
In this work, the uncertainty associated with the finite element discretization error is modeled following the Bayesian paradigm. First, a continuous formulation is derived, where a Gaussian process prior over the solution space is updated…
The randomly driven Burgers equation with pressure is considered as a 1D model of strong turbulence of compressible fluid. It is shown that infinitely small pressure provides a finite effect on the velocity and density statistics and this…
We present benchmark computations of dynamic poroelasticity modeling fluid flow in deformable porous media by a coupled hyperbolic-parabolic system of partial differential equations. A challenging benchmark setting and goal quantities of…
We numerically benchmark methods for computing harmonic maps into the unit sphere, with particular focus on harmonic maps with singularities. For the discretization we compare two different approaches, both based on Lagrange finite…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…
Gradient flows in the Wasserstein space have become a powerful tool in the analysis of diffusion equations, following the seminal work of Jordan, Kinderlehrer and Otto (JKO). The numerical applications of this formulation have been limited…
In models of oceanic and atmospheric flows, thermodynamic functions and conservative variables may be defined up to a certain degree of arbitrariness, in the sense that, for a given set of observable quantities such as pressure and…
The generally held view that a model of large-scale structure, formed by collisionless matter in the Universe, can be based on the matter model ``dust'' fails in the presence of multi-stream flow, i.e., velocity dispersion. We argue that…
Eulerian hydrodynamical simulations are a powerful and popular tool for modeling fluids in astrophysical systems. In this work, we critically examine recent claims that these methods violate Galilean invariance of the Euler equations. We…
A method is introduced for the construction of meshless discretization schemes which preserve Lie symmetries of the differential equations that these schemes approximate. The method exploits the fact that equivariant moving frames provide a…
Practical diffusion sampling is a numerical approximation problem: under a fixed inference budget, one must simulate a reverse-time ODE or SDE using only a limited number of denoising steps, so discretization error is often the dominant…
We consider a stochastic version of a system of coupled two equations formulated by Burgers with the aim to describe the laminar and turbulent motions of a fluid in a channel. The existence and uniqueness of the solution as well as the…
In this paper, semi-discrete numerical scheme for the approximation of the periodic Vlasov-viscous Burgers' system is developed and analyzed. The scheme is based on the coupling of discontinuous Galerkin approximations for the Vlasov…
Numerical models based on partial differential equations (PDE), or integro-differential equations, are ubiquitous in engineering and science, making it possible to understand or design systems for which physical experiments would be…
In this paper we propose optimisation methods for variational regularisation problems based on discretising the inverse scale space flow with discrete gradient methods. Inverse scale space flow generalises gradient flows by incorporating a…
We consider a model convection-diffusion problem and present useful connections between the finite differences and finite element discretization methods. We introduce a general upwinding Petrov-Galerkin discretization based on bubble…