A parallel interface tracking approach for evolving geometry problems

Yang, Fan; Chandra, Anirban; Tendulkar, Saurabh; Nastasia, Rocco; Oberai, Assad A.; Shephard, Mark S.; Sahni, Onkar

doi:10.1007/s00366-021-01386-8

Cited by 3 publications

(2 citation statements)

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“…[34][35][36][37] Further, VMS procedure has been employed to develop error estimation and apply mesh adaptation. [38][39][40][41][42][43][44][45] A rigorous and systematic VMS approach was developed by Hughes and Sangalli 3 for the advection-diffusion equation. At first, the fine-scale solution is defined based on an integral operator involving the fine-scale Green's function and the strong-form residual due to the coarse-scale solution.…”

Section: Introductionmentioning

confidence: 99%

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A dynamic variational multiscale method on unstructured meshes for stationary transport problems

Sahni

2023

Numerical Methods in Fluids

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Summary This paper presents a variational multiscale (VMS) based finite element method where the stabilization parameter is computed dynamically. The current dynamic procedure takes in a general structure/form of the stabilization parameter with unknown coefficients and computes them dynamically in a local fashion resulting in a dynamic VMS‐based finite element method. Thus, a static stabilization parameter with pre‐defined coefficients is not needed. A variational Germano identity (VGI) based local procedure suitable for unstructured meshes is developed to perform the dynamic computation in a local fashion. The local VGI based procedure is applied for each interior vertex in the mesh and unknown coefficients are first determined locally at each vertex, and subsequently, for each element a maximum value is taken over the vertices of the element. To make the current procedure practical, a coarser secondary solution is constructed from the primary coarse‐scale solution, which is done locally over a patch of elements around each interior vertex. Further, averaging steps are employed to make the local dynamic procedure robust. Currently, the new dynamic VMS formulation is applied to steady problems governed by the advection‐diffusion and incompressible Navier‐Stokes equations in both 1D and 2D to demonstrate its efficacy and effectiveness.

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Section: Introductionmentioning

confidence: 99%

“…Reduced order modeling has also been introduced using the VMS‐related stabilization approach and has shown benefit in solving flow problems 34‐37 . Further, VMS procedure has been employed to develop error estimation and apply mesh adaptation 38‐45 …”

Section: Introductionmentioning

confidence: 99%