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

doi:10.1007/s11709-018-0483-5

Frontiers of Structural and Civil Engineering

2019, Vol. 13

Issue (2): 429-455 https://doi.org/10.1007/s11709-018-0483-5

本期目录

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

Hassan YOUSEFI¹(

), Alireza TAGHAVI KANI², Iradj MAHMOUDZADEH KANI¹

¹. School of Civil Engineering, College of Engineering, University of Tehran, Tehran, 11155-4563, Iran
². Department of Civil Engineering, Arak University of Technology, Arak, 3818141167, Iran

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Abstract：

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.

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

收稿日期: 2017-07-30 出版日期: 2019-03-12

Corresponding Author(s): Hassan YOUSEFI

引用本文:

. [J]. Frontiers of Structural and Civil Engineering, 2019, 13(2): 429-455.
Hassan YOUSEFI, Alireza TAGHAVI KANI, Iradj MAHMOUDZADEH KANI. Multiscale RBF-based central high resolution schemes for simulation of generalized thermoelasticity problems. Front. Struct. Civ. Eng., 2019, 13(2): 429-455.

链接本文:

https://academic.hep.com.cn/fsce/CN/10.1007/s11709-018-0483-5
https://academic.hep.com.cn/fsce/CN/Y2019/V13/I2/429

RBF	$φ (r)$	Parameters	Order
Polyharmonic Splines (PS)	$r 2 n − d$ for $d$ odd $r 2 n − d ln ? (r)$ for $d$ even	$n ∈ ?, n 〉 d / 2$ $n ∈ ?, n 〉 d / 2$	$n$ $n$
Gaussians (G)	$exp ? (− c r 2)$		0
Multiquadries (MQ)	$(1 + c r 2) a$	$α 〉 0, α ∉ ?$	$[α]$
Inverse Multiquadries (IMQ)	$(1 + c r 2) a$	$α 〈 0$	0

Tab.1

Fig.1

$J max ?$	$N J max ?$	$C M S$ [min]
6	65	0.898
7	129	1.780
8	257	3.531
9	513	7.152

Tab.2

$J min ?$	$J max ?$	$N J max ?$	$r N, ∈ J max ?$ %	$N d t$	$C M S$ [min]
5	9	513	20.5	485	1.093
5	10	1025	9.8	970	2.488
5	11	2049	5.5	1940	4.862
5	12	4097	2.6	3880	10.165
5	13	8193	1.36	7760	23.731

Tab.3

		LT-third-order	CWENO-third-order
$J max ?$	$N J max ?$	$C M S$ [min]	$C M S$ [min]
6	65	0.346	0.361
7	129	0.679	0.756
8	257	1.331	1.427
9	513	2.651	2.871

Tab.4

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

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