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We propose an efficient algorithm for the immersed boundary method on distributed-memory architectures, with the computational complexity of a completely explicit method and excellent parallel scaling. The algorithm utilizes the…
We analyze a large number of high-order discrete velocity models for solving the Boltzmann-BGK equation for finite Knudsen number flows. Using the Chapman-Enskog formalism, we prove for isothermal flows a relation identifying the resolved…
Wall-bounded turbulent shear flows are known to exhibit universal small-scale dynamics that are modulated by large-scale flow structures. Strong pressure gradients complicate this characterization, however; they can cause significant…
This paper describes in detail the implementation of a finite element technique for solving the compressible Navier-Stokes equations that is provably robust and demonstrates excellent performance on modern computer hardware. The method is…
Recent progress indicates that highly symmetric recurring solutions of the Navier-Stokes equations, such as equilibria and periodic orbits, provide a skeleton for turbulence dynamics in state-space. Many of these solutions have been found…
The main objective of this paper is to present a generic modelling framework, for the diffusive mass transport through the turbulent, reactive boundary layer of multi-component fluid mixtures that precipitate on the wall. The modelling is…
In this paper, we study the transition threshold problem for the 2-D Navier-Stokes equations around the Poiseuille flow $(1-y^2,0)$ in a finite channel with Navier-slip boundary condition. Based on the resolvent estimates for the linearized…
Fluid simulation is an important research topic in computer graphics (CG) and animation in video games. Traditional methods based on Navier-Stokes equations are computationally expensive. In this paper, we treat fluid motion as point cloud…
We present a novel approach to hybrid RANS/LES wall modeling based on function enrichment, which overcomes the common problem of the RANS-LES transition and enables coarse meshes near the boundary. While the concept of function enrichment…
A new lattice Boltzmann method for simulating multiphase flows is developed theoretically. The method is adjusted such that its continuum limit is the Navier-Stokes equation, with a driving force derived from the Cahn-Hilliard free energy.…
We study a mathematical model of a compressible viscous fluid driven by stochastic forces under slip boundary conditions of friction type. We introduce a notion of a weak solution that is analytically and probabilistically consistent with…
The accuracy of Euler-Lagrange point-particle models employed in particle-laden fluid flow simulations depends on accurate estimation of the particle force through closure models. Typical force closure models require computation of the slip…
Direct numerical simulations (DNS) are performed for two wall-bounded flow configurations: laminar Couette flow at $Re=740$ and turbulent channel flow at $Re_{\tau}=180$, where $\tau$ is the shear stress at the wall. The top wall is smooth…
In this paper, we present a methodology to achieve high-fidelity simulations of chemically reacting hypersonic flows and demonstrate our numerical solver's capabilities on a selection of configurations. The numerical tools are developed…
We put forward the idea of defining vortex boundaries in planar flows as closed material barriers to the diffusive transport of vorticity. Such diffusive vortex boundaries minimize the leakage of vorticity from the fluid mass they enclose…
We present Aquarium, a differentiable fluid-structure interaction solver for robotics that offers stable simulation, accurately coupled fluid-robot physics in two dimensions, and full differentiability with respect to fluid and robot states…
The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier-Stokes equations coupled with a moving solid. This method presents the advantage to predict an…
A homogenization approach is proposed for the treatment of porous wall boundary conditions in the computation of compressible viscous flows. Like any other homogenization approach, it eliminates the need for pore-resolved fluid meshes and…
We present a parametric finite element approximation of two-phase flow with insoluble surfactant. This free boundary problem is given by the Navier--Stokes equations for the two-phase flow in the bulk, which are coupled to the transport…
This paper introduces JAX-FEM, an open-source differentiable finite element method (FEM) library. Constructed on top of Google JAX, a rising machine learning library focusing on high-performance numerical computing, JAX-FEM is implemented…