High Resolution Incompressible Flow Computations over Unstructured Mesh using SDWLS Gradients
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In practice, unstructured meshes are preferred choice for solving flows involving complex geometries. However obtaining the higher order accuracy on the unstructured mesh has always been a challenging task. In this paper, a new high-resolution scheme based on solution dependent weighted least squares (SDWLS) gradients is developed and applied to compute incompressible viscous flows over unstructured meshes. The artificial compressibility based formulation is utilized for incompressible Navier-Stokes equations. The dual time stepping approach is utilized to simulate time accurate incompressible flows. The Harten Lax and van Leer with contact for artificial compressibility (HLLC-AC) Riemann solver is used for evaluating convective fluxes whereas viscous fluxes are evaluated in central differencing manner. Sufficient numbers of benchmark problems are presented here to demonstrate the capability of the SDWLS based gradients scheme to produce high accuracy results over the unstructured meshes. From numerical experiments, it can be observed that the SDWLS based gradients scheme improves the solution accuracy as well as solution quality on unstructured mesh along with the efficiency of the present approach.
KeywordsHigher order accuracy Unstructured mesh SDWLS Incompressible flow Artificial compressibility method Steady/unsteady flow
This work has been partially supported by Science and Engineering Research Board (SERB)—Department of Science and Technology (DST), Government of India (ECR/2017/000476).
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