Industrial scale Large Eddy Simulations with adaptive octree meshes using immersogeometric analysis

Saurabh, Kumar; Gao, Boshun; Fernando, Milinda; Xu, Shanqin; Khanwale, Makrand A.; Khara, Biswajit; Hsu, Ming‐Chen; Krishnamurthy, Adarsh; Sundar, Hari; Ganapathysubramanian, Baskar

doi:10.1016/j.camwa.2021.05.028

Cited by 25 publications

(17 citation statements)

References 71 publications

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“…The DistTreeSort and TreeSort implementation is taken from Dendro [25]. All comparison with the immersed (IBM) method is performed using the open-source code [52] based on Saurabh et al [53]. Additionally, Matlab [41] is used for analyzing the condition number of matrices, and trimesh [20] is used to compute the signed distance.…”

Section: Resultsmentioning

confidence: 99%

“…This makes simulating non-cuboid domains non-trivial, with most approaches either relying on stretching (coordinate transforms) or using a much larger bounding box. Secondly, complex objects have to be immersed into the octree mesh [21,29,53], rather than being carved-out. Naively immersing the object in the octree can leave many elements that fall into the void regions.…”

Section: Related Workmentioning

confidence: 99%

“…The small volume resulted in most of the octants percolating close to the finest level before they can be discarded. Additionally, ray-tracing based In -Out test needs to be performed at each iteration of refinement, which is quite expensive [53]. Once the mesh is generated, we see a significant speedup in the overall solve time.…”

Section: Application: Classroom Airflow Simulationmentioning

confidence: 99%

“…Tree-based grid generation (quadtrees in 2D and octrees in 3D) is common in computational sciences [6,11,17,24,28,30,48,56,58] largely due to its simplicity and parallel scalability. The ability to efficiently refine (and coarsen) regions of interest using tree-based data structures have made it possible to deploy them on large-scale multi-physics simulations [2,3,14,24,32,33,37,37,49,53]. Existing algorithms for tree-based grid generation are mainly focused on axis-aligned hierarchical splitting on isotropic domains (i.e., spheres, squares, and cubes).…”

Section: Introductionmentioning

confidence: 99%

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Scalable adaptive PDE solvers in arbitrary domains

Saurabh,

Ishii,

Fernando

et al. 2021

Preprint

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Efficiently and accurately simulating partial differential equations (PDEs) in and around arbitrarily defined geometries, especially with high levels of adaptivity, has significant implications for different application domains. A key bottleneck in the above process is the fast construction of a 'good' adaptively-refined mesh. In this work, we present an efficient novel octree-based adaptive discretization approach capable of carving out arbitrarily shaped void regions from the parent domain: an essential requirement for fluid simulations around complex objects. Carving out objects produces an incomplete octree. We develop efficient top-down and bottom-up traversal methods to perform finite element computations on incomplete octrees. We validate the framework by (a) showing appropriate convergence analysis and (b) computing the drag coefficient for flow past a sphere for a wide range of Reynolds numbers (O (1−10 6 )) encompassing the drag crisis regime. Finally, we deploy the framework on a realistic geometry on a current project to evaluate COVID-19 transmission risk in classrooms.

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Section: Resultsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Application: Classroom Airflow Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Scalable adaptive PDE solvers in arbitrary domains

Saurabh,

Ishii,

Fernando

et al. 2021

Preprint

Self Cite

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“…3. Scalable octree-based adaptive mesh: We deploy the numerical scheme using a spatial discretization which utilizes mesh-free tree construction for parallel performance [20,21]. This allows us to track highly deforming interfaces in 2D and 3D using adaptive mesh refinement.…”

Section: Introductionmentioning

confidence: 99%

A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes

Khanwale,

Saurabh,

Ishii

et al. 2021

Preprint

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We present a projection-based framework for solving a thermodynamically-consistent Cahn-Hilliard Navier-Stokes system that models two-phase flows. In this work we extend the fully implicit method presented in Khanwale et al. [A fully-coupled framework for solving Cahn-Hilliard Navier-Stokes equations: Second-order, energy-stable numerical methods on adaptive octree based meshes., arXiv:2009.06628 (2020)], to a block iterative hybrid method. We use a projection-based semi-implicit time discretization for the Navier-Stokes and a fully-implicit time discretization for the Cahn-Hilliard equation. We use a conforming continuous Galerkin (cG) finite element method in space equipped with a residual-based variational multiscale (RBVMS) formulation. Pressure is decoupled using a projection step, which results in two linear positive semi-definite systems for velocity and pressure, instead of the saddle point system of a pressure-stabilized method. All the linear systems are solved using an efficient and scalable algebraic multigrid (AMG) method. We deploy this approach on a massively parallel numerical implementation using parallel octree-based adaptive meshes. The overall approach allows the use of relatively large time steps with much faster time-to-solve. We present comprehensive numerical experiments showing detailed comparisons with results from the literature for canonical cases, including the single bubble rise and Rayleigh-Taylor instability.

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A finite element level set method based on adaptive octree meshes for thermal free‐surface flows

Zhu

Fernando

et al. 2022

Numerical Meth Engineering

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We develop a parallel finite element computational framework based on the level set method and adaptive octree meshes for free‐surface flows. The discretized governing formulations are stabilized using a residual‐based variational multiscale method. We redistance the level set field and restore mass conservation after each time step. The octree mesh is adaptively refined according to the interface location, and the load is rebalanced across processes. The adaptive octree‐based level set method is verified and validated using a canonical problem of dam break without obstacle, and a mesh convergence study is carried out in this problem. The surface tension is further considered via a continuum surface force model in the method and validated using a problem of single bubble rising in ambient liquid. A parallel scaling analysis of this method is also performed for the bubble rising problem. The energy equation and Marangoni effect are finally considered in the method and validated using a problem of thermocapillary droplet migration with and without gravity. This work illustrates the ability of the framework to accurately model and predict free‐surface flows under various scenarios.

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Industrial scale Large Eddy Simulations with adaptive octree meshes using immersogeometric analysis

Cited by 25 publications

References 71 publications

Scalable adaptive PDE solvers in arbitrary domains

Scalable adaptive PDE solvers in arbitrary domains

A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes

A finite element level set method based on adaptive octree meshes for thermal free‐surface flows

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