Geodesic
Preconditioning of gas dynamics equations in compressible gas flow computations at low mach numbers
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 6, pp. 1058-1075

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Features of the simulation of low-velocity inviscid and viscous compressible gas flows are considered, and a finite-volume discretization of gas dynamics equations at low Mach numbers on unstructured meshes is discussed. Preconditioning based on the use of physical variables is used to speed up the convergence of time marching to a steady state and to improve the accuracy of the steady-state solution. The structure of the preconditioning matrix and the diagonalization of the Jacobian of the preconditioned system of equations are discussed. The capabilities of this approach are demonstrated using model gasdynamic simulations ing a wide range of Mach numbers. 
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     author = {K. N. Volkov and A. G. Karpenko},
     title = {Preconditioning of gas dynamics equations in compressible gas flow computations at low mach numbers},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1058--1075},
     publisher = {mathdoc},
     volume = {55},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_6_a12/}
}
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K. N. Volkov; A. G. Karpenko. Preconditioning of gas dynamics equations in compressible gas flow computations at low mach numbers. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 6, pp. 1058-1075. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_6_a12/