An accurate discretization for an inhomogeneous transport equation with arbitrary coefficients and source

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PASCAU A., ARICI M.

COMPUTERS & FLUIDS, cilt.125, ss.101-115, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 125
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1016/j.compfluid.2015.11.006
  • Dergi Adı: COMPUTERS & FLUIDS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.101-115
  • Anahtar Kelimeler: CFD, Nonhomogeneous transport equation, Convection diffusion, Integral solution, FINITE-DIFFERENCE SCHEME, EXACT NUMERICAL SCHEME
  • Kocaeli Üniversitesi Adresli: Evet

Özet

A new way of obtaining the algebraic relation between the nodal values in a general one-dimensional transport equation is presented. The equation can contain an arbitrary source and both the convective flux and the diffusion coefficient may vary arbitrarily. Contrary to the usual approach of approximating the derivatives involved, the algebraic relation is based on the exact solution written in integral terms. The required integrals can be speedily evaluated by approximating the integrand with Hermite splines or applying Gauss quadrature rules. The startling point about the whole procedure is that a very high accuracy can be obtained with few nodes, and more surprisingly, it can be increased almost up to machine accuracy by augmenting the number of quadrature points or the Hermite spline degree with little extra cost. (C) 2015 Elsevier Ltd. All rights reserved.