Delta waves and vacuum states in the vanishing pressure limit of Riemann solutions to Baer-Nunziato two-phase flow model

Qinglong Zhang

doi:10.3934/cpaa.2021104

Article Contents

2021, Volume 20, Issue 9: 3235-3258. Doi: 10.3934/cpaa.2021104

This issue Previous Article Fractional Yamabe solitons and fractional Nirenberg problem Next Article Admissible function spaces for weighted Sobolev inequalities

Delta waves and vacuum states in the vanishing pressure limit of Riemann solutions to Baer-Nunziato two-phase flow model

Qinglong Zhang

School of Mathematics and Statistics, Ningbo University, Ningbo, Zhejiang Province, 315211, China

Received: September 2020

Revised: May 2021

Early access: June 2021

Published: September 2021

The author is supported by K. C. Wong Magna Fund in Ningbo University

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Abstract

The phenomena of concentration and cavitation for the Riemann problem of the Baer-Nunziato (BN) two-phase flow model has been investigated in this paper. By using the characteristic analysis method, the formation of $ \delta- $waves and vacuum states are obtained as the pressure for both phases vanish in the BN model. The solid contact wave is carefully dealt. The comparison with the solutions of pressureless two-phase model shows that, two shock waves tend to a $ \delta- $shock solution, and two rarefaction waves tend to a two contact discontinuity solution when the solid contact discontinuity is involved. Moreover, the detailed Riemann solutions for two-phase flow model are given as the double pressure parameters vanish. This may contribute to the design of numerical schemes in the future research.

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Mathematics Subject Classification: Primary: 35L65, 35B25, 35Q35, 35L67; Secondary: 35L50.

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