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Moving bodies in compressible flow

A moving embedded boundary approach for the compressible Navier-Stokes equations

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

Solid composite propellant deflagration

Simulation of AP/HTPB burn in Alamo

Ammonium perchlorate (AP) particles packed in a hydroxyl-terminated polybutadiene (HTPB) binder are a common type of solid composite propellant (SCP) used in solid rocket motors. Deflagration of AP/HTPB and the resulting burn front regression produces a complex burn/unburned interface, often with islands of binder left behind. A phase field model for SCP deflagration was implemented in Alamo. The movie shows the interface regression of a 3D sample of AP/HTPB.

A diffuse interface method for solid-phase modeling of regression behavior in solid composite propellants, B Kanagarajan, JM Quinlan, B Runnels, Combustion and Flame, 2022

Phase field modeling of solid phase AP/HTPB to determine the effect of particle distribution on regression rate, B Kanagarjan, JM Quinlan, B Runnels, AIAA SciTech, San Diego, CA, January 2022

Image courtesy of Brandon Runnels, Solid Mechanics Research Group, University of Colorado, Colorado Springs, CO.

Stokes Breaking Wave

Incompressible multiphase flow with high density ratio and high Reynolds number

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.

Self-propelled swimming eel

A DLM immersed boundary method framework for solving fluid-structure interaction problems

We present an adaptive implementation of the distributed Lagrange multiplier (DLM) immersed boundary (IB) method on multilevel collocated grids for solving single- and multiphase fluid-structure interaction (FSI) problems. The capabilities and robustness of the computational framework are validated against a variety of benchmarking problems. A three-dimensional swimming eel is shown here.

Yadong Zeng, Amneet Pal Singh Bhalla, and Lian Shen. "A subcycling/non- subcycling time advancement scheme-based DLM immersed boundary method framework for solving single and multiphase fluid–structure interaction problems on dynamically adaptive grids." Computers and Fluids 238 (2022): 105358.

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

Atomization of a Liquid Jet

All-Mach, Compressible Multiphase Flow

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.

Microstructure Evolution Using Solid Mechanics

Simulation of microstructure evolution in a polycrystalline solid using Alamo

In this simulation, the multiphase field method is used and the evolution equation is integrated explicitly. Microstructure evolution is driven by boundary curvature (as in high temperature annealing) which causes coarsening. The microstructure is initialized using a Voronoi tesselation with 40 initial grains. The simulation has three levels of mesh refinement, and was run on the Texas Advanced Computing Center Stampede2 computer with 512 MPI processes for 10 hours.

Image courtesy of Brandon Runnels, Solid Mechanics Research Group, University of Colorado, Colorado Springs, CO.

Detonation Propagation and Failure

Modeling Compressible Reactive Gas Dynamics

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

Three-dimensional Hydrogen Jet

Detailed adaptive simulation of a burning Hydrogen jet with RNS

Three-dimensional premixed Hydrogen/Air flame computed with the RNS code. RNS is a block-structured AMR code that solves the compressible reactive Navier-Stokes equations with detailed models for the chemistry, and is based on high-order numerical methods (AMLSDC and WENO) that achieve fourth-order accuracy in both time and space.

  • A Fourth-Order Adaptive Mesh Refinement Algorithm for the Multicomponent, Reacting Compressible Navier-Stokes Equations , M. Emmett, E. Motheau, W. Zhang, M. Minion and J. B. Bell, submitted for publication, 2018.[arxiv]
Image courtesy Emmanuel Motheau

Yield-stress fluids

Capturing transient behaviour of strain-rate-dependent rheological models

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.

Dimethyl Ether Jet

Detailed adaptive simulation of a burning Dimethyl Ether jet with RNS

An instantaneous snapshot of the temperature field of a Dimethyl Ether flame computed with the RNS code. RNS is a block-structured AMR code that solves the compressible reactive Navier-Stokes equations with detailed models for the chemistry, and is based on high-order numerical methods (AMLSDC and WENO) that achieve fourth-order accuracy in both time and space.

  • A Fourth-Order Adaptive Mesh Refinement Algorithm for the Multicomponent, Reacting Compressible Navier-Stokes Equations , M. Emmett, E. Motheau, W. Zhang, M. Minion and J. B. Bell, submitted for publication, 2018.[arxiv]
Image courtesy Emmanuel Motheau

Laser Wakefield Acceleration

Modeling the interaction between plasma and electrons

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.

Shock Reflection

Compressible Gas Dynamics with AMR Embedded Boundaries

A compressible gas dynamics shock reflection using an embedded boundary representation of the ramp. The colors represent the density field. There are 3 total levels of refinement. The code for this simulation is available in the AMReX tutorial, amrex/Tutorials/EB/CNS/Exec/ShockRef/.

Black hole Collisions

Code Generation and Simulation of the Spacetime Evolution of Black Hole Mergers

The video to the right 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 wtih 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.

Black Hole Advertising

Simulation of Large Systems of Black Holes with Heavily Designed Initial Conditions

The video to the left shows an amusing application of the STvAR code generators and AMReX to spacetime evolution. Click on the image to see what happens and then read the description below.

The video shows the simulation of a very large system of black holes, starting from heavily designed initial conditions using the STvAR package. The entire video is run in reverse.

Videos and Images courtesy of Adam Peterson and Don Wilcox.