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

Anna Karina Fontes Gomes, Margarete Oliveira Domingues, Odim Mendes


This work is concerned with the numerical simulation of the Kelvin-Helmholtz instability using a two-dimensional resistive magnetohydrodynamics model in the context of 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 compare our solution with the solution of the well known astrophysics FLASH code to verify our code in respect to this reference.


Magnetohydrodynamics, Kelvin-Helmholtz instability, Adaptive multiresolution analysis, Numerical simulation

Full Text:



A. Frank, T. W. Jones, D. Ryu, and J. B. Gaalaas. The magnetohydrody-

namic Kelvin-Helmholtz instability: A two-dimensional numerical study. The

Astrophysical Journal, 460:777, 1996.

A. Harten. Multiresolution representation of data: a general framework. SIAM Journal of Numerical Analysis, 33(3):385–394, 1996.

O. Roussel, K. Schneider, A. Tsigulin, and H. Bockhorn. A conservative fully adaptive multiresolution algorithm for parabolic {PDEs}. Journal of Computational Physics, 188(2):493 – 523, 2003.

A. K. F. Gomes. Análise multirresolução adaptativa no contexto da resolução numérica de um modelo de magnetohidrodinâmica ideal. Master’s thesis, Instituto Nacional de Pesquisas Espaciais (INPE), São José dos Campos, 2012.

M. O. Domingues, A. K. F. Gomes, S. M. Gomes, O. Mendes, B. Di Pierro,

and K. Schneider. Extended generalized lagrangian multipliers for magnetohydrodynamics using adaptive multiresolution methods. ESAIM Proceedings, 43:95–107, 2013.

A. K. F. Gomes, M. O. Domingues, K. Schneider, O. Mendes, and R. Deiterding. An adaptive multiresolution method for ideal magnetohydrodynamics using divergence cleaning with parabolic–hyperbolic correction. Applied Numerical Mathematics, 95:199 – 213, 2015.

B. Fryxell, K. Olson, P. Ricker, F. X. Timmes, M. Zingale, D. Q. Lamb, P. MacNeice, R. Rosner, J. W. Truran, and H. Tufo. FLASH: An adaptive mesh

hydrodynamics code for modeling astrophysical thermonuclear flashes. The

Astrophysical Journal Supplement Series, 131:273–334, November 2000.

R. J. Hosking and R. L. Dewar. Fundamental Fluid Mechanics and Magnetohydrodynamics. Springer Singapore, 2016.

M. O. Domingues, R. Deiterding, S. M. Gomes, and K. Schneider. Comparison of adaptive multiresolution and adaptive mesh refinement applied to simulations of the compressible euler equations. SIAM Journal on Scientific Computing, in press.

K. G. Powell, P. L. Roe, T. J. Linde, T. I. Gombosi, and D. L. De Zeeuw. A Solution-Adaptative Upwind Scheme for Ideal Magnetohydrodynamics. Journal of Computational Physics, 154:284–309, 1999.

A. Dedner, F. Kemm, D. Kröner, C.-D. Munz, T. Schnitzer, and M. Wesenberg. Hyperbolic divergence cleaning for the MHD equations. Journal of Computational Physics, 175:645–673, 2002.

A. Mignone and P. Tzeferacos. A second-order unsplit Godunov scheme for cell-centered MHD: The CTU-GLM scheme. Journal of Computational Physics, 229(6):2117–2138, 2010.

T. Miyoshi and K. Kusano. A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics. Journal of Computational Physics, 208:315–344, 2005.

E. F. Toro. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Springer-Verlag Berlin Heidelberg, 1999.

M. O. Domingues, S. M. Gomes, O. Roussel, and K. Schneider. Adaptive

multiresolution methods. ESAIM Proceedings, 34:1–96, 2011.

E. F. D. Evangelista, M. O. Domingues, O. Mendes, and O. D. Miranda. A brief study of instabilities in the context of space magnetohydrodynamic simulations. Revista Brasileira de Ensino de Física, 38(1), 2016.


Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM


  • There are currently no refbacks.

Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)


Indexed in:




Desenvolvido por:

Logomarca da Lepidus Tecnologia