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This chapter addresses how to devise high-order, positivity-preserving finite difference schemes for unsteady compressible Navier-Stokes equations. We consider the equation of states beyond ideal gas law, including the stiffened-gas equation of state used to represent non-ideal gases and liquids. After presenting the viscous stresses, viscous work terms, and heat conduction terms, we discuss how to compute them using a general Lax-Friedrichs type discretization that yields positivity-preserving solutions.

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Schemes for Compressible Two-Fluid Navier-Stokes Equations

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  • 发表日期：

    2025年

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  • Khosro Shahbazi

摘要

This chapter addresses how to devise high-order, positivity-preserving finite difference schemes for unsteady compressible Navier-Stokes equations. We consider the equation of states beyond ideal gas law, including the stiffened-gas equation of state used to represent non-ideal gases and liquids. After presenting the viscous stresses, viscous work terms, and heat conduction terms, we discuss how to compute them using a general Lax-Friedrichs type discretization that yields positivity-preserving solutions.