This paper accompanies the publication of the open source lattice Boltzmann solver VIRTUALFLUIDS [DOI: 10.5281/zenodo.10283048]. Key features of VIRTUALFLUIDS are the cumulant collision operator, the ability to run multi-scale simulations based on compact interpolation grid refinement and its implementations for both GPU and massively parallel CPU systems. The differences in data structure for the different systems are explained in detail. PROGRAM SUMMARY Program Title: VIRTUALFLUIDS CPC Library link to program files: https://doi.org/10.17632/tfzdnz7vwx.1 Developer's repository link: https://git.rz.tu-bs.de/irmb/VirtualFluids.git Licensing provisions: GPLv3 Programming language: C++, C, Cuda, Python, CMake Nature of problem: High resolution transient computational fluid dynamics with applications in urban and environmental flows, wind engineering, porous materials, aero-acoustics etc. is implemented in a sustainable software environment. Solution method: Fluid flow is simulated with the super-convergent cumulant lattice Boltzmann method with compact interpolation grid refinement. The software is designed for massively parallel computation on various computer architectures, ranging from desktop computers to high performance clusters. GPU computation is enabled by a CUDA simulation kernel. A sustainable code basis is obtained through continuous integration and a wide range of tests i.e. unit tests, regression test, etc.

In this work, transitional flow characteristics in gyroidal structures are investigated. For specified flow rates corresponding to a range of Reynolds numbers from 400 to 7000, the pressure drop between inlet and outlet is determined. The experimentally obtained pressure drops are computed numerically with the cumulant lattice Boltzmann method which serves as a solver for the weakly compressible flow. Different grid resolutions are used for the simulations in order to investigate grid convergence. In order to create an accurate geometric representation of the setup, we use a newly developed formalism to describe gyroids with finite thickness based on an implicit volume representation. This representation avoids the expensive and inaccurate triangulation of the gyroid structure. Consequently, it avoids the problems encountered with mesh-based representations by providing a compact, local, and therefore inherently parallel representation for geometric computations such as classification of nodes and the computation of subgrid distances.

In this paper, we present a framework for the modeling and simulation of a subset of physical/chemical processes occurring on different spatial and temporal scales in porous materials. In order to improve our understanding of such processes on multiple spatio-temporal scales, small-scale simulations of transport and reaction are of vital importance. Due to the geometric complexity of the pore space and the need to consider a representative elementary volume, such simulations require substantial numerical resolutions, leading to potentially huge computation times. An efficient parallelization of such numerical methods is thus vital to obtain results in acceptable wall-clock time. The goal of this paper was to improve available approaches based on lattice Boltzmann methods (LBMs) to reliably and accurately predict the combined effects of mass transport and reaction in porous media. To this end, we relied on the factorized central moment LBM as a second-order accurate approach for modeling transport. In order to include morphological changes due to the dissolution of the solid phase, the volume of fluid method with the piece-wise linear interface construction algorithm was employed. These developments are being integrated into the LBM research code VirtualFluids. After the validation of the analytic test cases, we present an application of diffusion-controlled dissolution for a pore space obtained from computer tomography (CT) scans.

Modeling of fluids with complex rheology in the lattice Boltzmann method (LBM) is typically realized through the introduction of an effective viscosity. For fluids with a yield stress behavior, such as so-called Bingham fluids, the effective viscosity has a singularity for low shear rates and may become negative. This is typically avoided by regularization such as Papanastasiou’s method. Here we argue that the effective viscosity model can be re-interpreted as a generalized equilibrium in which no violation of the stability constraint is observed. We implement a Bingham fluid model in a three-dimensional cumulant lattice Boltzmann framework and compare the direct analytic effective viscosity/generalized equilibrium method to the iterative approach first introduced by Vikhansky which avoids the singularity in viscosity that can arise in the analytic method. We find that both methods obtain similar results at coarse resolutions. However, at higher resolutions the accuracy of the regularized method levels off while the accuracy of the direct method continuously improves. We find that the accuracy of the proposed direct method is not limited by the singularity in viscosity indicating that a regularization is not strictly necessary.

The simulation of fire is a challenging task due to its occurrence on multiple space-time scales and the non-linear interaction of multiple physical processes. Current state-of-the-art software such as the Fire Dynamics Simulator (FDS) implements most of the required physics, yet a significant drawback of this implementation is its limited scalability on modern massively parallel hardware. The current paper presents a massively parallel implementation of a Gas Kinetic Scheme (GKS) on General Purpose Graphics Processing Units (GPGPUs) as a potential alternative modeling and simulation approach. The implementation is validated for turbulent natural convection against experimental data. Subsequently, it is validated for two simulations of fire plumes, including a small-scale table top setup and a fire on the scale of a few meters. We show that the present GKS achieves comparable accuracy to the results obtained by FDS. Yet, due to the parallel efficiency on dedicated hardware, our GKS implementation delivers a reduction of wall-clock times of more than an order of magnitude. This paper demonstrates the potential of explicit local schemes in massively parallel environments for the simulation of fire.

This review summarizes the rigorous mathematical theory behind the lattice Boltzmann equation (LBE). Relevant properties of the Boltzmann equation and a derivation of the LBE from the Boltzmann equation are presented. A summary of some important LBE models is provided. Focus is given to results from the numerical analysis of the LBE as a solver for the nearly incompressible Navier-Stokes equations with appropriate boundary conditions. A number of numerical results are provided to demonstrate the efficacy of the lattice Boltzmann method.

In this paper a rotating grid technique for the cumulant lattice Boltzmann model is presented. The rotating object is embedded in a rotating mesh that communicates with an enclosing stationary mesh via compact quadratic interpolation. On the rotating mesh, Coriolis and centrifugal forces model the rotation with respect to the outer Eulerian frame of reference. A proper rotation of all moments is imposed in the interface between the moving and the static grid. The fluid flow is simulated by the cumulant lattice Boltzmann model. Profiles of pressure, velocity and shear stress are compared with the analytical solution of Taylor–Couette flow and we demonstrate that our scheme is second order accurate in space. As a second numerical benchmark, lift and drag coefficients for a rotating ellipsoidal cylinder in a laminar flow are simulated and successfully compared to a reference solution.

We present a comprehensive analysis of the cumulant lattice Boltzmann model with the three-dimensional Taylor–Green vortex benchmark at Reynolds number 1600. The cumulant model is investigated in several different variants, using regularization, fourth-order convergent diffusion and fourth-order convergent advection with and without limiters. In addition, a cumulant model combined with a WALE sub-grid scale model is being evaluated. The turbulence model is found to filter out the high wave number contributions from the energy spectrum and the enstrophy, while the non-filtered cumulant methods show good correspondence to spectral simulations even for the high wave numbers. The application of the WALE turbulence model appears to be counter productive for the Taylor–Green vortex at a Reynolds number of 1600. At much higher Reynolds numbers ( $${\hbox {Re}}=160{,}000$$ ) a deviation from the ideal Kolmogorov theory can be observed in the absence of an explicit turbulence model. Cumulant models with fourth-order convergent diffusion show much better results than single relaxation time methods.

Porous trailing edges have been proposed as a means to reduce acoustic emissions from aircraft wings. However, the influence of the porous material on the aerodynamic performance of the wing has to be investigated. In this work we report DNS/LES simulations of turbulent flow over a DLR-F16 wing profile at a Reynolds number of $$10^6$$ using a cumulant lattice Boltzmann method. The cumulant LBM is implemented in the object-oriented framework VirtualFluids. Due to the requirement of resolving the boundary layer, the resulting simulation setups consist of more than two billion grid nodes and $$72.9\times 10^{9}$$ degrees of freedom distributed on a locally refined three-dimensional grid requiring massively parallel simulations. We discuss modeling and scaling aspects of our approach and present computational results including experimental validation.

Gas-kinetic schemes (GKS) have been developed as a kinetic Finite-Volume approach to computational fluid dynamics. The GKS a priori allows to obtain approximate solutions of the fully compressible Navier-Stokes equations. In our contribution we show simulation results of compressible natural convection at large temperature differences and low Mach numbers beyond the applicable range of the Boussinesq approximation. The simulations were performed on non-uniform quadrilateral and unstructured triangular grids. The dependence of the critical Rayleigh number on the temperature difference for compressible Rayleigh-Bénard convection, predicted by theory, is accurately reproduced. Moreover, heat transfer in a buoyancy driven square cavity with differentially heated sides at large Rayleigh numbers and large temperature differences is investigated. Temperature and velocity profiles as well as Nusselt numbers show good agreement with benchmark results in literature. After validating the scheme for thermal compressible convection, we investigate unsteady natural convection at a Rayleigh number of Ra=5⋅109 and at a large temperature difference of Th/Tc=4. We find that compressibility has a leading influence on the stability of the boundary layers, such that the flow at the heated wall becomes unstable, whereas the flow at the cooled wall remains stable. This phenomenon has not yet received much attention.

A hybrid Lattice Boltzmann(LB)-finite difference(FD) numerical scheme for the simulation of reacting flows at low Mach numbers is presented. The FD solver is used to model the energy and species fields while the LB model computes the flow field. The proposed LB solver is a modified version of the classical iso-thermal weakly compressible LB scheme with the hydrodynamic pressure as its zeroth-order moment instead of density, recovering the well-known low Mach number approximation for thermo-compressible flows. The proposed numerical approach is used to model a variety of test-cases ranging from 1-D to 3-D configurations, involving premixed and non-premixed flames. In all cases results obtained by this solver are shown to agree very well with reference data.

For the past two decades a slowly growing consensus has been that rising temperature is being caused by increases in carbon dioxide (CO2) in the Earth's atmosphere. What is less consensual is what to do about it. Solutions range from reducing emissions to various ways to capture CO2 (from effluents of power plants, as plants, etc.) and store it away from the atmosphere. The problem is of such magnitude that it is likely that we will need many methods. Also some methods would cause draconian harm to global economies. This work is about the storage part of the reducing of CO2 in the atmosphere. There have been many methods proposed for storing CO2: in vegetation, at the bottom of oceans, in land farms, and in subsurface formations. The latter is particularly prominent given the large estimated volume in porous formation in the Earth, and the 50-year old experience in injecting CO2 for enhanced oil recovery. This report is about the science behind subsurface storage, called here geological carbon storage or GCS. Effective GCS requires that billions of metric tons of CO2 be injected into storage reservoirs annually. GCS feasibility requires balancing the opposing impacts of large emplacement (injection) rates without compromising caprock seal integrity during injection. Once injected, the challenge is to assure the injected CO2 remains permanently stored. Under most conditions, CO2 is in a supercritical state, or scCO2. scCO2 is immiscible with the subsurface brine and has a factor of ten smaller viscosity, leading to the development of two-phase fluid flow and scCO2 bypassing. After the injection of large volumes of scCO2, the pore pressure, state of stress, chemical, thermal, and biological steady-state or equilibrium conditions in the subsurface are disrupted, which may lead to unpredictable behavior because the responses to these changes are often non-linear. Current challenges for efficient and reliable scCO2 storage are: (1) sustaining large injection rates; (2) using available pore space efficiently, and (3) controlling undesired or unexpected behavior, such as scCO2 leakage. Various aspects of these challenges are addressed by collaborative projects within Center for Frontiers in Subsurface Energy Security (CFSES). Challenge 1 Sustaining large storage rates To offset the annual CO2 emissions of in the United States, ~7 billion metric tons of CO2 must be injected into the storage reservoirs annually. Injected CO2 forms a plume that starts spreading, displacing originally resident brine, though inefficiently so. Because of its low viscosity, and buoyant forces, a CO2 plume rises to the reservoir rock-caprock interface. Injecting large volumes of scCO2 at sufficiently high rates into subsurface storage formations leads to increases in pore pressures, potential expansion of the reservoir rock, and may result in fracturing of the reservoir rock and/or caprock. CFSES research uses existing and new experimental and modeling approaches to identify chemical-physical controls on the permeability and pore pressure dynamics, anticipating geomechanical (fracturing) events, predicting multi-phase flow patterns and trapping of CO2. Challenge 2 – Using pore space with unprecedented efficiency Since large volumes of scCO2 are to be stored, the volume available in storage reservoirs must be used efficiently. Storage efficiency is defined as a fraction of pore space occupied by carbon dioxide. Current estimates are that less than 5 percent of available pore volume is available for storage because scCO2, having a smaller density and viscosity than reservoir brine, tends to form viscous fingers, and bypass available pore space. This flow regime results in a CO2 plume spreading over large areas in subsurface. The research goal in Challenge 2 is to advance the fundamental understanding of two-phase flow through porous media, including molecular-to meter- scale experimental and modeling approaches. This work leads to novel strategies to ensure that injected CO2 occupies more than 5% of the pore space, ideally up to 50%. Challenge 3 – Controlling undesired or unexpected behavior Following the injection of scCO2, the subsurface reservoir re-equilibrates to different physical and chemical states. This re-equilibration in space and time could lead to unexpected and/or undesired behavior: fracturing of reservoir rock and/or caprock, development of preferential flow paths, CO2 leakage (to the surface or overlaying fresh water reservoirs), induced seismicity, and activation of faults. One of the main research goals of CFSES was to advance the fundamental understanding of how individual chemical and physical processes are coupled. We particularly focused on the chemical-mechanical coupling, and flow-mechanical coupling. We collected experimental and modeling data to determine the temporal and spatial scales of the coupled processes, which may lead to pore collapse caused by creep, activation of fractures and faults, chemically-induced fracture propagation, and self-focusing of scCO2 flow.

In this paper, we construct and analyze a family of quadratic finite volume element schemes over triangular meshes for elliptic equations. This family of schemes cover some existing quadratic schemes. For these schemes, by element analysis, we find that each element matrix can be split as two parts : the first part is the element stiffness matrix of the standard quadratic finite element method, while the second part is a tensor product of two vectors. Thanks to this finding, we obtain a sufficient condition to ensure the existence, uniqueness and coercivity result of the finite volume element solution on triangular meshes. More interesting is that, the above condition has a simple and analytic expression, and only relies on the interior angles of each triangular element. Based on this result, a minimum angle condition, better than some existing ones, can be obtained. Moreover, based on the coercivity result, we prove that the finite volume element solution converges to the exact solution with an optimal convergence rate in H1 norm. Finally, some numerical examples are provided to validate the theoretical findings.

We present an efficient algorithm of a two-dimensional Gas Kinetic Scheme (GKS) suitable for General Purpose Graphics Processing Units (GPGPUs). The algorithm features conservative second order quadtree-type refinement for Cartesian meshes and nested time stepping. The implementation is validated for several incompressible and thermal compressible test cases in the low Mach (Ma) number regime. We find that heat transfer for high Rayleigh (Ra) number and turbulent convection can be simulated correctly. Finally, we demonstrate a simulation of a Rayleigh-Benard setup with Ra = 10(13) that qualitatively resembles the conditions of fire on a room scale. The implementation delivers a performance of more than one billion cell updates per second. (C) 2019 Elsevier Ltd. All rights reserved.

This work explores the feasibility of real-time large-eddy simulations of flow over urban canopies at the neighborhood scale. The cumulant lattice Boltzmann method is employed using a single General Purpose Graphic Processing Unit (GPGPU). In order to demonstrate the validity and efficiency of this approach we simulate wind flow in a neighborhood of Basel. Simulation results are validated against measurements from the Basel Urban Boundary Layer Experiment (BUBBLE) and are compared to previous CFD simulations. Turbulence statistics are found to be in agreement with corresponding tower measurements according to several validation metrics. While quantitative comparisons are limited to the six measurement locations of the field measurements, the available data supports the conjecture that real-time simulation of urban air flow is feasible at the neighborhood scale with the proposed numerical technique.