A skew-symmetric energy and entropy stable formulation of the compressible Euler equations

• We show that a specific skew-symmetric form of nonlinear hyperbolic problems leads to energy and entropy bounds. Next, we exemplify by considering the compressible Euler equations in primitive variables, transform them to skew-symmetric form and show how to obtain energy and entropy estimates. Finally we show that the skew-symmetric formulation lead to energy and entropy stable discrete approximations if the scheme is formulated on summation-by-parts form.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Nonlinear hyperbolic problems

Skew-symmetric form

Compressible Euler equations

Energy stability

Entropy stability

Summation-by-parts

Publication and Content Type

ref (subject category)

art (subject category)