Geodesic
High accuracy scheme for solving nonlinear aeroacoustics problems on unstructured meshes
Matematičeskoe modelirovanie, Tome 19 (2007) no. 7, pp. 56-66

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The paper represents a multi-parameter family of higher accuracy (up to the 6th order) schemes for solving 1D linear transport equation. The schemes are constructed on the base of central-difference approximation of space derivatives with adding the upwinding dissipation and the linear Runge-Kutta method of arbitrarily high order of accuracy for the time integration. A detailed analysis of computational errors and an example of test computation are given. 
@article{MM_2007_19_7_a4,
     author = {I. V. Abalakin and T. K. Kozubskaya},
     title = {High accuracy scheme for solving nonlinear aeroacoustics problems on unstructured meshes},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {56--66},
     publisher = {mathdoc},
     volume = {19},
     number = {7},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2007_19_7_a4/}
}
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I. V. Abalakin; T. K. Kozubskaya. High accuracy scheme for solving nonlinear aeroacoustics problems on unstructured meshes. Matematičeskoe modelirovanie, Tome 19 (2007) no. 7, pp. 56-66. http://geodesic.mathdoc.fr/item/MM_2007_19_7_a4/