Simulating fluid dynamics on a quantum computer is intrinsically difficult due to the nonlinear
and non-Hamiltonian nature of the Navier-Stokes equation (NSE). We propose a framework …

The animation of delicate vortical structures of gas and liquids has been of great interest in
computer graphics. However, common velocity-based fluid solvers can damp the vortical …

We propose a novel gauge fluid solver based on Clebsch wave functions to solve
incompressible fluid equations. Our method combines the expressive power of Clebsch …

We propose a novel Clebsch method to simulate the free-surface vortical flow. At the center
of our approach lies a level-set method enhanced by a wave-function correction scheme …

We present a compendium of Hodge decompositions of vector fields on tetrahedral meshes
embedded in the 3D Euclidean space. After describing the foundations of the Hodge …

We derive the spin Euler equation for ideal flows by applying the spherical Clebsch
mapping. This equation is based on the spin vector, a unit vector field encoding vortex lines …

Clebsch maps encode velocity fields through functions. These functions contain valuable
information about the velocity field. For example, closed integral curves of the associated …

We demonstrate that, if a globally smooth virtual circulation-preserving velocity exists,
Kelvin's and Helmholtz's theorems can be extended to some non-ideal flows which are …

This paper presents a new representation of curve dynamics, with applications to vortex
filaments in fluid dynamics. Instead of representing these filaments with explicit curve …

The large-eddy simulation (LES) is a promising tool in the computational fluid dynamics, with
a balance between the computational cost and accuracy [1-4]. The LES solves the flow …