An <i>r</i>-factor algorithm for TVD schemes on unstructured grids

GAO Xin; ZHANG Xiaomin; WU Qiong; ZHAO Zhipeng; LIU Yang; OU Junfeng; LIU Jian

doi:10.7638/kqdlxxb-2024.0033

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An r-factor algorithm for TVD schemes on unstructured grids

更新时间：2026-05-28

- An r-factor algorithm for TVD schemes on unstructured grids
- Vol. 43, Issue 10, Pages: 44-58(2025)
- 作者机构：
  
  1. 重庆大学航空航天学院,重庆,400044
  2. 重庆大学非均质材料力学重庆市重点实验室,重庆,400044
  3. 重庆长安汽车股份有限公司,重庆,400023
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2024.0033
  CLC： V211.3;O35
- Published：2025
- 稿件说明：
移动端阅览
高鑫, 张晓敏, 吴琼, 等. 基于非结构化网格下TVD格式的一种r因子算法[J]. 空气动力学学报, 2025, 43(10): 44−58.

GAO Xin, ZHANG Xiaomin, WU Qiong, et al. An r-factor algorithm for TVD schemes on unstructured grids[J]. 2025, 43(10): 44-58. DOI: 10.7638/kqdlxxb-2024.0033.
高鑫, 张晓敏, 吴琼, 等. 基于非结构化网格下TVD格式的一种r因子算法[J]. 空气动力学学报, 2025, 43(10): 44−58. DOI： 10.7638/kqdlxxb-2024.0033

GAO Xin, ZHANG Xiaomin, WU Qiong, et al. An r-factor algorithm for TVD schemes on unstructured grids[J]. 2025, 43(10): 44-58. DOI: 10.7638/kqdlxxb-2024.0033. DOI：

摘要

针对对流主导问题的数值模拟，提出了一种改进的

因子算法，以实现TVD（total variational diminishing）格式在非结构化网格中的扩展。新算法将面中心到辅助逆风节点的距离考虑在内，以实现更合理的远逆风节点位置预测；通过包含更多逆风信息的插值方法和采取考虑实际点与辅助点之间的物理值差异的方法来提高TVD格式的精度；并避免引入复杂的向量计算过程以提高效率。非结构化网格下对流主导问题的基准测试结果表明，相比于现有的其他算法，新

因子算法在精度和效率方面具有更好的性能。

Abstract

To realize the implementation of TVD schemes on unstructured grids

an improved

-factor algorithm is proposed for the numerical simulation of the convection-dominated problems. The distance from the face center to the auxiliary upwind node is considered in the new

-factor algorithm

which achieves more reasonable prediction of the far-upwind node position. The accuracy of TVD schemes on unstructured grids is improved by invoking an interpolation scheme that contains more upwind information and considering the physical deviation between the actual nodes and the auxiliary nodes. Meanwhile

the computational efficiency is improved by avoiding the introduction of complex vector computation procedures in

the new algorithm. Benchmark testing results of the convection-dominated problems on unstructured grids indicate that the new

factor algorithm outperforms existing ones in terms of both accuracy and efficiency.

关键词

Keywords

references

UBBINK O , ISSA R I. A method for capturing sharp fluid interfaces on arbitrary meshes[J]. Journal of Computational Physics, 1999, 153(1): 26−50. doi: 10.1006/jcph.1999.6276

ZHANG D, JIANG C B, LIANG D F, et al. A refined volume-of-fluid algorithm for capturing sharp fluid interfaces on arbitrary meshes[J]. Journal of Computational Physics, 2014, 274: 709−736. doi: 10.1016/j.jcp.2014.06.043

DENNER F, VAN WACHEM B G M. Compressive VOF method with skewness correction to capture sharp interfaces on arbitrary meshes[J]. Journal of Computational Physics, 2014, 279: 127−144. doi: 10.1016/j.jcp.2014.09.002

LI J, ZHANG Q, ZHAI Z J, et al. An improved r-factor algorithm for total variational diminishing (TVD) schemes on two-dimension non-uniform unstructured grids[J]. International Journal for Numerical Methods in Fluids, 2021, 93(5): 1446−1467. doi: 10.1002/fld.4937

ZHANG D, JIANG C B, LIANG D F, et al. A review on TVD schemes and a refined flux-limiter for steady-state calculations[J]. Journal of Computational Physics, 2015, 302: 114−154. doi: 10.1016/j.jcp.2015.08.042

ZHANG D, JIANG C B, CHENG L, et al. A refined r -factor algorithm for TVD schemes on arbitrary unstructured meshes[J ] . International Journal for Numerical Methods in Fluids, 2016, 80(2): 105−139. doi: 10.1002/fld.4073

HARTEN A. High resolution schemes for hyperbolic conservation laws[J]. Journal of Computational Physics, 1983, 49(3): 357−393. doi: 10.1016/0021-9991(83)90136-5

SWEBY P K. High resolution schemes using flux limiters for hyperbolic conservation laws[J]. SIAM Journal on Numerical Analysis, 1984, 21(5): 995−1011. doi: 10.1137/0721062

VAN LEER B. Towards the ultimate conservative difference scheme I. The quest of monotonicity[C]//3rd International Conference on Numerical Methods in Fluid Mechanics, 1973. doi: 10.1007/BFb0118673

WATERSON N P. Development of a bounded higher-order convection scheme for general industrial applications[M]. Belgium:Von Karman Institute for Fluid Dynamics, 1994.

VAN ALBADA G D, VAN LEER B, ROBERTS JR W W. A comparative study of computational methods in cosmic gas dynamics[J]. Astronomy and Astrophysics, 1982, 108(1): 76−84.

KOREN B. Upwind discretization of the steady Navier-Stokes equations[J]. International Journal for Numerical Methods in Fluids, 1990, 11(1): 99−117. doi: 10.1002/fld.1650110107

VAN LEER B. Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme[J]. Journal of Computational Physics, 1974, 14(4): 361−370. doi: 10.1016/0021-9991(74)90019-9

ALVES M A, OLIVEIRA P J, PINHO F T. A convergent and universally bounded interpolation scheme for the treatment of advection[J]. International journal for numerical methods in fluids, 2003, 41(1): 47−75. doi: 10.1002/fld.428

GASKELL P H, LAU A K C. Curvature-compensated convective transport: SMART, a new boundedness-preserving transport algorithm[J]. International Journal for Numerical Methods in Fluids, 1988, 8(6): 617−641. doi: 10.1002/fld.1650080602

ROE P L. Some contributions to the modelling of discontinuous flows[C]// 15th Summer Seminar on Applied Mathematics, 1983.

FERREIRA V G, DE QUEIROZ R A B, LIMA G A B, et al. A bounded upwinding scheme for computing convection-dominated transport problems[J]. Computers and Fluids, 2012, 57: 208−224. doi: 10.1016/j.compfluid.2011.12.021

FERREIRA V G, KUROKAWA F A, DE QUEIROZ R A B, et al. Assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems[J]. International Journal for Numerical Methods in Fluids, 2009, 60(1): 1−26. doi: 10.1002/fld.1875

BRUNER C, WALTERS R, BRUNER C, et al. Parallelization of the Euler equations on unstructured grids[C]//Proc of the 13th Computational Fluid Dynamics Conference, Snowmass Village, CO. Reston, Virginia: AIAA, 1997: 1894. doi: 10.2514/6.1997-1894

DARWISH M S, MOUKALLED F. TVD schemes for unstructured grids[J]. International Journal of Heat and Mass Transfer, 2003, 46(4): 599−611. doi: 10.1016/S0017-9310(02)00330-7

ZHANG D, JIANG C B, YANG C, et al. Assessment of different reconstruction techniques for implementing the NVSF schemes on unstructured meshes[J]. International Journal for Numerical Methods in Fluids, 2014, 74(3): 189−221. doi: 10.1002/fld.3846

LI L X, LIAO H S, QI L J. An improved r-factor algorithm for TVD schemes[J]. International Journal of Heat and Mass Transfer, 2008, 51(3-4): 610−617. doi: 10.1016/j.ijheatmasstransfer.2007.04.051

HOU J, SIMONS F, HINKELMANN R. A new TVD method for advection simulation on 2D unstructured grids[J]. International Journal for Numerical Methods in Fluids, 2013, 71(10): 1260−1281. doi: 10.1002/fld.3709

DENG Y Y, LIU Y K, ZHANG D, et al. Modified far-upwind reconstruction methods for the implementation of NVSF schemes on unstructured grids[J]. Numerical Heat Transfer, Part B: Fundamentals, 2023, 83(5): 292−322. doi: 10.1080/10407790.2023.2174220

KONG J, XIN P, SHEN C J, et al. A high-resolution method for the depth-integrated solute transport equation based on an unstructured mesh[J]. Environmental Modelling and Software, 2013, 40: 109−127. doi: 10.1016/j.envsoft.2012.08.009

LEONARD B P, DRUMMOND J E. Why you should not use 'Hybrid', 'Power-Law' or related exponential schemes for convective modelling—there are much better alternatives[J]. International Journal for Numerical Methods in Fluids, 1995, 20(6): 421−442. doi: 10.1002/fld.1650200602

ARMALY BF, DURST F, PEREIRA JC, SCHÖNUNG B. Experimental and theoretical investigation of backward-facing step flow[J]. Journal of fluid Mechanics, 1983, 127: 473−496.

BORIS J P, BOOK D L. Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works[J]. Journal of Computational Physics, 1973, 11(1): 38−69. doi: 10.1016/0021-9991(73)90147-2

ZHANG K, FENG X F, JING H F, et al. An improved MRT-LBM and investigation to the transition and periodicity of 2D lid-driven cavity flow with high Reynolds numbers[J]. Chinese Journal of Physics, 2023, 84: 51−65. doi: 10.1016/j.cjph.2023.04.006

GHIA U, GHIA K N, SHIN C T. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method[J]. Journal of computational physics, 1982, 48(3): 387−411. doi: 10.1016/0021-9991(82)90058-4

ERTURK E, CORKE T C, GÖKÇÖL C. Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers[J]. International Journal for Numerical Methods in Fluids, 2005, 48(7): 747−774. doi: 10.1002/fld.953

GUERRERO J. Numerical simulation of the unsteady aerodynamics of flapping flight[D]. Genova, Italy: University of Genoa, 2009.

CALHOUN D. A cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions[J]. Journal of Computational Physics, 2002, 176(2): 231−275. doi: 10.1006/jcph.2001.6970

RUSSELL D, WANG Z J. A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow[J]. Journal of Computational Physics, 2003, 191(1): 177−205. doi: 10.1016/S0021-9991(03)00310-3

BRAZA M, CHASSAING P, HA H M. Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder[J]. Journal of Fluid Mechanics, 1986, 165(1): 79−130. doi: 10.1017/S0022112086003014

CHOI J I, OBEROI R C, EDWARDS J R, et al. An immersed boundary method for complex incompressible flows[J]. Journal of Computational Physics, 2007, 224(2): 757−784. doi: 10.1016/j.jcp.2006.10.032

LANEY C B. Computational gasdynamics[M]. Cambridge, UK: Cambridge University Press, 1998. doi: 10.1017/cbo9780511605604

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An r-factor algorithm for TVD schemes on unstructured grids

DOI：10.7638/kqdlxxb-2024.0033

摘要

Abstract

关键词

Keywords

references