Simulation of the growth of a filamentous fungal network (mycelium) on the surface of a nutrient-containing agar plate. The mycelium is composed of individual segments (hyphae) that are linked together to form the network. The simulation utilizes both the continuum multiresolution features of the AMReX framework as well as the functionality for simulating the behavior of individual particles. The transport of nutrients in the agar plate is modelled using continuum diffusion and the hyphal segments are modelled as individual particles with a set of complicated non-isotropic pairwise interactions. The paper, "Three-dimensional modeling of hyphal fusion, branching and nutrient tranport in filamentous fungi" is available HERE.

Image courtesy of Bruce Palmer, Connah Johnson, and William Cannon (PNNL).

We developed a highly efficient CPUs/GPUs solver for the fully resolved simulation of particle-laden flows by combining the lattice Boltzmann method for fluid and the immersed boundary method for fluid-structure interaction into the framework of adaptive mesh refinement. The animation shows that 500 spherical particles settling in a narrow channel, with a weak Rayleigh–Taylor type instability. The simulation was carried out on NVIDIA A100 GPUs, and the details of the governing equations and numerical methods can be found in the paper "An immersed boundary lattice Boltzmann method on block-structured adaptive grids for the simulation of particle-laden flows on CPUs/GPUs" available HERE.

Image courtesy of Yaning Wang, Yadong Zeng, and Zhaohui Liu.

The animation shows a three-dimensional, test bed simulation of a thunderstorm performed using the Energy Research and Forecasting (ERF) codebase. Warm and moist air rises due to buoyancy and condenses to form cloud water (1e-5 kg/(kg of dry air) isocontour of cloud water is shown in white). Cloud water, through the processes of autoconversion and accretion, forms rain water drops (1e-4 kg/(kg of dry air) isocontour of rain is shown in blue) that fall down to the ground as precipitation. Cloud water and rain water also evaporate to form water vapor, which rises and condenses, thus creating a feedback loop that leads to the development of a thunderstorm. This simulation was performed on NVIDIA A100 GPUs on Perlmutter. Details of the governing equations and numerical methods can be found in the ERF documentation.

"ERF: Energy Research and Forecasting", Ann Almgren et al., The Journal of Open Source Software, 2023.

Video and Image courtesy: Mahesh Natarajan, Aaron Lattanzi and Ann Almgren, LBNL; Eliot Quon, NREL.

A computational technique has been developed to perform compressible flow simulations involving moving boundaries using an embedded boundary approach within the block- structured adaptive mesh refinement (SAMR) framework of AMReX. We leverage the SAMR capability to obtain quantitatively accurate results whilst using robust, second- order finite volume schemes. A conservative, unsplit, cut-cell approach is utilized and a ghost-cell approach is developed for computing the flux on the moving, embedded boundary faces. A third-order least-squares formulation has been developed to compute the wall velocity gradients, and was found to significantly improve the performance of the solver in terms of the quantitative comparison of surface quantities such as the skin friction coefficient. The algorithm was implemented within the Compressible Navier-Stokes (CNS) solver of AMReX. Various test cases are performed to validate the method, and compared with analytical, experimental, and other numerical results in literature. Inviscid and viscous test cases are performed that span a wide regime of flow speeds. The judicious use of adaptive mesh refinement with appropriate refinement criteria to capture the regions of interest leads to well-resolved flow features, and good quantitative comparison is observed with the results available in literature.

"A moving embedded boundary approach for the compressible Navier-Stokes equations in a block-structured adaptive refinement framework", Mahesh Natarajan, Ray Grout, Weiqun Zhang, and Marc Day, Journal of Computational Physics, 11315, 2022.

Image Courtesy: Mahesh Natarajan, Ray Grout, Weiqun Zhang, and Marc Day.

A dynamic and complex breaking wave problem is simulated with the help of the framework AMReX. The movie shows the evolution of the air–water interface obtained from the three-level subcycling case. Grid patches are dynamically refined around the interface as time evolves.

Zeng, Yadong, et al. "A parallel cell-centered adaptive level set framework for efficient simulation of two-phase flows with subcycling and non-subcycling." Journal of Computational Physics 448 (2022): 110740.

Image courtesy of Yadong Zeng and Lian Shen, Fluid Mechanics Lab, University of Minnesota.

Simulation of primary atomization of a liquid (water) jet in a Mach 1.94 supersonic crossflow (air). An all-Mach, compressible multiphase flow solver is developed within the framework of AMReX. The Interface Reconstruction Library (IRL) was used to implement an efficient, discretely conservative, unsplit, geometric volume-of-fluid (VOF) transport scheme. The liquid-gas interface in each mixed cell is represented using piecewise linear interface calculation (PLIC). The movie shows streamwise velocity contours with the 4 level mesh and an isocontour of VOF with the finest level of refinement.

A Robust All-Mach Multiphase Flow Algorithm for High-Fidelity Simulations of Compressible Atomization, M.B. Kuhn and O. Desjardins, ILASS-Americas 30th Annual Conference on Liquid Atomization and Spray Systems, Tempe, AZ, May 2019.

An all-Mach multiphase flow solver using block-structured AMR, M. Natarajan, R. Chiodi, M. Kuhn and O. Desjardins, ILASS-Americas 30th Annual Conference on Liquid Atomization and Spray Systems, Tempe, AZ, May 2019.

Image courtesy M. Natarajan, R. Chiodi, M. B. Kuhn, O. Desjardins, Computational Thermo-Fluids Laboratory, Cornell University.

Simulation of detonation propagation and failure by diffraction with HyBurn. The detonation is initiated in a reactant layer bounded by high-temperature products that have a very low acoustic impedance. The simulation used with 6 levels of refinement with a refinement ratio of 256 between the finest and coarsest levels. The detonation is initiated by a series of high-pressure, high-temperature spots. The detonation propagates steadily until it encounters a step change in the height of the reactant layer. The leading shock of the detonation weakens as it diffracts around the step, resulting in a decoupled shock and flame. The movie shows the temperature field and follows the detonation.

Image courtesy Brayden Roque, Hsiao-Chi Li, and Ryan Houim.

Lid-driven cavity problem for a Papanastasiou-regularised Bingham fluid with Reynold's number 1000, Bingham number 1 and regularisation parameter 0.0025. The heatmap shows the effective viscosity distribution, while the black contour lines illustrate the location of the surface where the stress magnitude equals a characteristic threshold value. In order to accurately resolve this yield surface, we utilise adaptive mesh refinement with stress-triggered cell tagging in three layers.

Time-dependent viscoplastic fluid flow simulations in two and three dimensions, K. Sverdrup, N. Nikiforakis and A. Almgren, in preparation, 2018, arXiv:1803.00417.

Image courtesy of Knut Sverdrup, Laboratory for Scientific Computing, University of Cambridge.

Simulation of laser wakefield acceleration performed with WarpX. The laser pulse propagates from left to right in a uniform plasma. A moving window is used, i.e. the simulation box travels at the speed of light to follow the laser pulse. The central slice of plasma electrons is shown as transparent white dots. A cavity free of plasma electrons forms in the laser wake, where an electron bunch (solid white dots) is accelerated. The colormap shows the longitudinal electric field in the wake. The white box in the center shows the mesh-refined area.

Image courtesy Maxence Thévenet & the WarpX team.

The video shows the spacetime evolution of two equal mass spinning (Kerr) black holes merging into a single black hole with outward propagating gravitational waves. The evolution was simulated using the Z4c formulation of the Einstein equations with 6 levels of AMR in AMReX. The complex equations of motion were generated using the STvAR package, designed for converting symbolic/tensorial forms to executable code for AMReX.

The STvAR package was inspired by Professor Zach Etienne and the NRPy+ project at West Virginia University.

Videos and Images courtesy of Adam Peterson and Don Wilcox.