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An approach for constructing a low-dissipation numerical method is described.The method is based on a combination of the operator-splitting method, Godunovmethod, and piecewise-parabolic method on the local stencil. Numerical methodwas tested on a standard suite of hydrodynamic test problems. In addition, theperformance of the method is demonstrated on a global test problem showing thedevelopment of a spiral structure in a gravitationally unstable gaseousgalactic disk.

Using the PPML approach for constructing a low-dissipation, operator-splitting scheme for numerical simulations of hydrodynamic flows