A high-order vertex-based central ENO finite-volume scheme for three-dimensional compressible flows

Charest, Marc R.J.; Canfield, Thomas R.; Morgan, Nathaniel R.; Waltz, Jacob; Wohlbier, John G.

doi:10.1016/j.compfluid.2015.03.001

Title: A high-order vertex-based central ENO finite-volume scheme for three-dimensional compressible flows

Journal Article · Wed Mar 11 00:00:00 EDT 2015 · Computers and Fluids

DOI:https://doi.org/10.1016/j.compfluid.2015.03.001· OSTI ID:1214833

Charest, Marc R.J. ^[1]; Canfield, Thomas R. ^[1]; Morgan, Nathaniel R. ^[1]; Waltz, Jacob ^[1]; Wohlbier, John G. ^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

High-order discretization methods offer the potential to reduce the computational cost associated with modeling compressible flows. However, it is difficult to obtain accurate high-order discretizations of conservation laws that do not produce spurious oscillations near discontinuities, especially on multi-dimensional unstructured meshes. A novel, high-order, central essentially non-oscillatory (CENO) finite-volume method that does not have these difficulties is proposed for tetrahedral meshes. The proposed unstructured method is vertex-based, which differs from existing cell-based CENO formulations, and uses a hybrid reconstruction procedure that switches between two different solution representations. It applies a high-order k-exact reconstruction in smooth regions and a limited linear reconstruction when discontinuities are encountered. Both reconstructions use a single, central stencil for all variables, making the application of CENO to arbitrary unstructured meshes relatively straightforward. The new approach was applied to the conservation equations governing compressible flows and assessed in terms of accuracy and computational cost. For all problems considered, which included various function reconstructions and idealized flows, CENO demonstrated excellent reliability and robustness. Up to fifth-order accuracy was achieved in smooth regions and essentially non-oscillatory solutions were obtained near discontinuities. The high-order schemes were also more computationally efficient for high-accuracy solutions, i.e., they took less wall time than the lower-order schemes to achieve a desired level of error. In one particular case, it took a factor of 24 less wall-time to obtain a given level of error with the fourth-order CENO scheme than to obtain the same error with the second-order scheme.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1214833

Alternate ID(s):: OSTI ID: 1254185

Report Number(s):: LA-UR-14-23047; PII: S0045793015000651

Journal Information:: Computers and Fluids, Vol. 114, Issue C; ISSN 0045-7930

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 11 works

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