We analyze the appearance of delta shock wave and vacuum state in the vanishing pressure limit of Riemann solutions to the non-isentropic generalized Chaplygin gas equations. 非等エントロピー一般化チャプリギンガス方程式のリーマン解の消失圧力限界におけるデルタ衝撃波と真空状態の出現を分析します。

The Vanishing Pressure Limit of Riemann Solutions to the Non-Isentropic Euler Equations for Generalized Chaplygin Gas

The phenomena of concentration and cavitation and the formation of delta shock waves and vacuum states in vanishing pressure limits of solutions to the generalized Chaplygin Euler equations of compressible fluid flow are analyzed. 圧縮性流体の一般化されたChaplyginオイラー方程式の解の圧力限界の消失における集中とキャビテーションの現象およびデルタ衝撃波と真空状態の形成を分析します。

Concentration and cavitation in the vanishing pressure limit of solutions to the generalized Chaplygin Euler equations of compressible fluid flow

During the process of vanishing pressure, the phenomenon of concentration can be identified and analyzed when the two-shock Riemann solution tends to a delta shock wave solution as well as the phenomenon of cavitation also being captured and observed when the two-rarefaction-wave Riemann solution tends to a two-contact-discontinuity solution with a vacuum state between them. 圧力が消失する過程で、2つの衝撃波のリーマン解がデルタ衝撃波の解になる傾向がある場合の集中の現象と、2つの希薄化波のリーマンの場合のキャビテーションの現象もキャプチャして観察できます。解は、それらの間に真空状態がある2接触不連続解になる傾向があります。

Solutions with concentration and cavitation to the Riemann problem for the isentropic relativistic Euler system for the extended Chaplygin gas

In the presence of a finite three-body scattering amplitude, the superfluid gas at this point exhibits sound modes whose velocity scales linearly with density while the compressibility diverges \$\sim p^{-1/3}\$ in the limit of vanishing pressure \$p\$. 有限の3体散乱振幅が存在する場合、この時点での超流動ガスは、速度が密度に比例して変化するサウンドモードを示し、圧縮率は消失圧力の限界で\$ \ sim p ^{-1/3}\$発散します。 p\$。

Quantum unbinding near a zero temperature liquid-gas transition