Ideal and Resistive Magnetohydrodynamic Two-Dimensional Simulation of the Kelvin-Helmholtz Instability in the Context of Adaptive Multiresolution Analysis

GOMES, A.K.F.; DOMINGUES, M.O.; MENDES, O.

doi:10.5540/tema.2017.018.02.0317

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Articles • TEMA (São Carlos) 18 (2) • Aug 2017 • https://doi.org/10.5540/tema.2017.018.02.0317 copy

Ideal and Resistive Magnetohydrodynamic Two-Dimensional Simulation of the Kelvin-Helmholtz Instability in the Context of Adaptive Multiresolution Analysis

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

This work is concerned with the numerical simulation of the Kelvin-Helmholtz instability using an ideal and resistive two-dimensional magnetohydrodynamics model in the context of an adaptive multiresolution approach. The Kelvin-Helmholtz instabilities are caused by a velocity shear and normally expected in a layer between two fluids with different velocities. Due to its complexity, this kind of problem is a well-known test for numerical schemes and it is important for the verification of the developed code. The aim of this paper is to verify the implemented numerical model with the well-known astrophysics FLASH code.

Keywords:
magnetohydrodynamics; Kelvin-Helmholtz instability; adaptive multiresolution analysis; numerical simulation; scientific computing

ρ	p	u_x	u_y	u_z	B_x	B_y	B_z
1.0	50.0	$u_{x}^{0}$	$u_{y}^{0}$	0.0	1.0	0.0	0.0

CARMEN code	2*Variables	Errors
CARMEN code	2*Variables	ℒ¹ (× 10^-2 )	ℒ² (× 10^-4 )	ℒ^∞ (× 10^-1 )
FV	ρ	0.29	0.14	0.89
	p	18.25	10.53	67.87
	_^ux	6.57	4.32	22.86
	_^uy	3.34	1.74	8.38
	_^Bx	4.04	2.09	10.69
	_^By	1.65	0.76	3.22
MR	ρ	0.30	0.14	1.00
	p	18.38	9.10	60.11
	_^ux	6.72	4.14	21.98
	_^uy	3.82	1.83	8.43
	_^Bx	4.08	1.81	8.63
	_^By	1.91	0.80	3.37

CARMEN code	Variables	Errors
CARMEN code	Variables	ℒ¹ (× 10^-3 )	ℒ² (× 10^-4 )	ℒ^∞ (× 10^-2 )
FV	ρ	0.13	0.06	0.37
	p	7.57	3.56	7.39
	_^ux	2.72	1.47	4.05
	_^uy	1.56	0.90	2.33
	_^Bx	2.26	1.27	1.94
	_^By	1.18	0.64	1.07
MR	ρ	0.81	0.38	0.66
	p	55.89	26.04	46.27
	_^ux	10.04	5.58	13.57
	_^uy	9.91	5.62	12.37
	_^Bx	7.27	4.06	5.82
	_^By	3.38	1.89	2.62

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[1] *Corresponding author: Anna Karina Fontes Gomes