Frontiers of Structural and Civil Engineering

, Volume 13, Issue 2, pp 429–455 | Cite as

Multiscale RBF-based central high resolution schemes for simulation of generalized thermoelasticity problems

  • Hassan YousefiEmail author
  • Alireza Taghavi Kani
  • Iradj Mahmoudzadeh Kani
Research Article


In this study, average-interpolating radial basis functions (RBFs) are successfully integrated with central high-resolution schemes to achieve a higher-order central method. This proposed method is used for simulation of generalized coupled thermoelasticity problems including shock (singular) waves in their solutions. The thermoelasticity problems include the LS (systems with one relaxation parameter) and GN (systems without energy dissipation) theories with constant and variable coefficients. In the central high resolution formulation, RBFs lead to a reconstruction with the optimum recovery with minimized roughness on each cell: this is essential for oscillation-free reconstructions. To guarantee monotonic reconstructions at cell-edges, the nonlinear scaling limiters are used. Such reconstructions, finally, lead to the total variation bounded (TVB) feature. As RBFs work satisfactory on non-uniform cells/grids, the proposed central scheme can handle adapted cells/grids. To have cost effective and accurate simulations, the multiresolution–based grid adaptation approach is then integrated with the RBF-based central scheme. Effects of condition numbers of RBFs, computational complexity and cost of the proposed scheme are studied. Finally, different 1-D coupled thermoelasticity benchmarks are presented. There, performance of the adaptive RBF-based formulation is compared with that of the adaptive Kurganov-Tadmor (KT) second-order central high-resolution scheme with the total variation diminishing (TVD) property.


central high resolution schemes RBFs higher order accuracy generalized thermoelasticity multiresolution-based adaptation 


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The authors gratefully acknowledge the financial support of Iran National Science Foundation (INSF).


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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Hassan Yousefi
    • 1
    Email author
  • Alireza Taghavi Kani
    • 2
  • Iradj Mahmoudzadeh Kani
    • 1
  1. 1.School of Civil Engineering, College of EngineeringUniversity of TehranTehranIran
  2. 2.Department of Civil EngineeringArak University of TechnologyArakIran

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