2019/12/13 by Oliver F Oxtoby, Alexandros Syrakos, Oxtoby, Oliver +9
Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Heat and Mass Transfer in Porous Media #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1912.08064
openalex publication_date 2019/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A new discretisation scheme for the gradient operator, suitable for use in\nsecond-order accurate Finite Volume Methods (FVMs), is proposed. The derivation\nof this scheme, which we call the Taylor-Gauss (TG) gradient, is similar to\nthat of the least-squares (LS) gradients, whereby the values of the\ndifferentiated variable at neighbouring cell centres are expanded in truncated\nTaylor series about the centre of the current cell, and the resulting equations\nare summed after being weighted by chosen vectors. Unlike in the LS gradients,\nthe TG gradients use vectors aligned with the face normals, resembling the\nGreen-Gauss (GG) gradients in this respect. Thus, the TG and LS gradients\nbelong in a general unified framework, within which other gradients can also be\nderived. The similarity with the LS gradients allows us to try different\nweighting schemes (magnitudes of the weighting vectors) such as weighting by\ninverse distance or face area. The TG gradients are tested on a variety of\ngrids such as structured, locally refined, randomly perturbed, and with high\naspect ratio. They are shown to be at least first-order accurate in all cases,\nand are thus suitable for use in second-order accurate FVMs. In many cases they\ncompare favourably over existing schemes.\n