Low Mach Number Fluctuating Hydrodynamics of Diffusively Mixing Fluids

We formulate low Mach number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with different density and transport coefficients. These equations eliminate the fast isentropic fluctuations in pressure associated with the propagation of sound waves by replacing the equation of state with a local thermodynamic constraint. We demonstrate that the low Mach number model preserves the spatio-temporal spectrum of the slower diffusive fluctuations. We develop a strictly conservative finite-volume spatial discretization of the low Mach number fluctuating equations in both two and three dimensions. We construct several explicit Runge-Kutta temporal integrators that strictly maintain the equation of state constraint. The resulting spatio-temporal discretization is second-order accurate deterministically and maintains fluctuation-dissipation balance in the linearized stochastic equations. We apply our algorithms to model the development of giant concentration fluctuations in the presence of concentration gradients, and investigate the validity of common simplications neglecting the spatial non-homogeneity of density and transport properties. We perform simulations of diffusive mixing of two fluids of different densities in two dimensions and compare the results of low Mach number continuum simulations to hard-disk molecular dynamics simulations. Excellent agreement is observed between the particle and continuum simulations of giant fluctuations during time-dependent diffusive mixing

Stochastic Transport in Upper Ocean Dynamics

This open access proceedings volume brings selected, peer-reviewed contributions presented at the Stochastic Transport in Upper Ocean Dynamics (STUOD) 2021 Workshop, held virtually and in person at the Imperial College London, UK, September 20–23, 2021. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography

Large-eddy simulation of compressible flows using the stretched-vortex model and a fourth-order finite volume scheme on adaptive grids

2022 Spring.Includes bibliographical references.State-of-the-art engineering workflows are becoming increasingly dependent on accurate large-eddy simulations (LES) of compressible, turbulent flows for off-design conditions. Traditional CFD algorithms for compressible flows rely on numerical stabilization to handle unresolved physics and/or steep gradient flow features such as shockwaves. To reach higher levels of physical-fidelity than previously attainable, more accurate turbulence models must be properly incorporated into existing, high-order CFD codes in a manner that preserves the stability of the underlying algorithm while fully realizing the benefits of the turbulence model. As it stands, casually combining turbulence models and numerical stabilization degrades LES solutions below the level achievable by using numerical stabilization alone. To effectively use high-quality turbulence models and numerical stabilization simultaneously in a fourth-order-accurate finite volume LES algorithm, a new method based on scale separation is developed using adaptive grid technology for the stretched-vortex subgrid-scale (SGS) LES model. This method successfully demonstrates scheme-independent and grid-independent LES results at very-high-Reynolds numbers for the inviscid Taylor-Green vortex, the temporally-evolving double-shear-flow, and decaying, homogeneous turbulence. Furthermore, the method clearly demonstrates quantifiable advantages of high-order accurate numerical methods. Additionally, the stretched-vortex LES wall-model is extended to curvilinear mapped meshes for compressible flow simulations using adaptive mesh refinement. The capabilities of the wall-model combined with the stretched-vortex SGS LES model are demonstrated using the canonical zero-pressure-gradient flat-plate turbulent boundary layer. Finally, the complete algorithm is applied to simulate flow-separation and reattachment over a smooth-ramp, showing high-quality solutions on extremely coarse meshes

Stochastic Transport in Upper Ocean Dynamics

This open access proceedings volume brings selected, peer-reviewed contributions presented at the Stochastic Transport in Upper Ocean Dynamics (STUOD) 2021 Workshop, held virtually and in person at the Imperial College London, UK, September 20–23, 2021. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography