TY - JOUR

T1 - A fully implicit Navier-Stokes algorithm using an unstructured grid and flux difference splitting

AU - Knight, Doyle D.

PY - 1994/12

Y1 - 1994/12

N2 - An implicit algorithm is developed for the two-dimensional, compressible, laminar Navier-Stokes equations using an unstructured grid of triangles. A sell-centered data structure is employed with the flow variables stored at the centroids of the triangles. The algorithm is based on Roe's flux difference split method for the inviscid fluxes, and a discrete representation of the viscous fluxes and heat transfer using Gauss' Theorem. Linear reconstruction of the flow variables to the cell faces, employed for the inviscid terms, provides second-order spatial accuracy. Interpolation of the flow variables to the nodes is achieved using a second-order accurate method. Temporal discretization employs Euler, trapezoidal or 3-point backward differencing. The complete, exact Jacobian of the inviscid and viscous terms is derived. The algorithm is applied to the Riemann Shock tube problem, a supersonic laminar boundary layer on a flat plate, and subsonic viscous flow past an NACA0012 airfoil. Results are in excellent agreement with theory and previous computations.

AB - An implicit algorithm is developed for the two-dimensional, compressible, laminar Navier-Stokes equations using an unstructured grid of triangles. A sell-centered data structure is employed with the flow variables stored at the centroids of the triangles. The algorithm is based on Roe's flux difference split method for the inviscid fluxes, and a discrete representation of the viscous fluxes and heat transfer using Gauss' Theorem. Linear reconstruction of the flow variables to the cell faces, employed for the inviscid terms, provides second-order spatial accuracy. Interpolation of the flow variables to the nodes is achieved using a second-order accurate method. Temporal discretization employs Euler, trapezoidal or 3-point backward differencing. The complete, exact Jacobian of the inviscid and viscous terms is derived. The algorithm is applied to the Riemann Shock tube problem, a supersonic laminar boundary layer on a flat plate, and subsonic viscous flow past an NACA0012 airfoil. Results are in excellent agreement with theory and previous computations.

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U2 - https://doi.org/10.1016/0168-9274(94)00043-3

DO - https://doi.org/10.1016/0168-9274(94)00043-3

M3 - Article

SN - 0168-9274

VL - 16

SP - 101

EP - 128

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 1-2

ER -