Geodesic
Dynamic adaptation method in gasdynamic simulations with nonlinear heat conduction
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 11, pp. 2067-2080

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A dynamic adaptation method is applied to gas dynamics problems with nonlinear heat conduction. The adaptation function is determined by the condition that the energy equation is quasi-stationary and the grid point distribution is quasi-uniform. The dynamic adaptation method with the adaptation function thus determined and a front-tracking technique are used to solve the model problem of a piston moving in a heat-conducting gas. It is shown that the results significantly depend on the thermal conductivity chosen. The numerical results obtained on a 40-node grid are compared with self-similar solutions to this problem. 
@article{ZVMMF_2008_48_11_a14,
     author = {P. V. Breslavskiy and V. I. Mazhukin},
     title = {Dynamic adaptation method in gasdynamic simulations with nonlinear heat conduction},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2067--2080},
     publisher = {mathdoc},
     volume = {48},
     number = {11},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_11_a14/}
}
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P. V. Breslavskiy; V. I. Mazhukin. Dynamic adaptation method in gasdynamic simulations with nonlinear heat conduction. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 11, pp. 2067-2080. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_11_a14/