Geodesic
Space-marching method for solving the steady Euler equations on adaptive grids
Matematičeskoe modelirovanie, Tome 9 (1997) no. 10, pp. 83-97.

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A space-marching noniterative method using an adaptive grid approach is proposed for solving 2D Euler equations describing supersonic steady gas flows without separation. The adaptive grid is obtained as a result of the minimization of the functionals of smoothness, orthogonality and adaptivity [l].The weight function of the functional of adaptivity is chosen as a function of absolute value of the density gradient. 2D Euler equations are approximated by using an implicit 2nd order finite-difference scheme both in marching and in crossflow directions. The derivatives in the marching direction are calculated by applying the implicit Richardson scheme. For the approximation of the crossflow derivatives the 2nd order symmetry TVD scheme [2] is used. Numerical calculations of supersonic gas flows show that the present method is very efficient in terms of computer time and accuracy. 
@article{MM_1997_9_10_a36,
     author = {N. K. Yamaleev},
     title = {Space-marching method for solving the steady {Euler} equations on adaptive grids},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {83--97},
     publisher = {mathdoc},
     volume = {9},
     number = {10},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1997_9_10_a36/}
}
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N. K. Yamaleev. Space-marching method for solving the steady Euler equations on adaptive grids. Matematičeskoe modelirovanie, Tome 9 (1997) no. 10, pp. 83-97. http://geodesic.mathdoc.fr/item/MM_1997_9_10_a36/