A relaxation approach to the coupling of a two-phase fluid with a linear-elastic solid

Abstract

A recently developed coupling strategy for two nonconservative hyperbolic systems is employed to investigate a collapsing vapor bubble embedded in a liquid near a solid. For this purpose, an elastic solid modeled by a linear system of conservation laws is coupled to the two-phase Baer-Nunziato-type model for isothermal fluids, a nonlinear hyperbolic system with non-conservative products. For the coupling of the two systems the Jin-Xin relaxation concept is employed and embedded in a second order finite volume scheme. For a proof of concept simulations in one space dimension are performed.

Figures (7)

• Figure 1: The coupled relaxation system at the interface. The coupling states $\bar{U}_R$, $\bar{V}_R$, $U_L$ and $V_L$ constitute suitable boundary data with respect to the (numerical) traces $\bar{U}_0^-$, $\bar{V}_0^-$, $U_0^+$, $V_0^+$ and satisfy a coupling condition encoded in $\Phi_Q$.
• Figure 2: Discretization of the real line as used in our finite volume scheme.
• Figure 3: Numerical solution in terms of pressure and velocity showing seven time instances until $t =300 \mu s$ over the computational domain with coupling interface at $x=0$, where the structure and the fluids interact.
• Figure 4: Volume fractions of water vapor ($\alpha_1$) and liquid water ($\alpha_2$) in the numerical solution until $t =300 \mu s$ over the multiphase fluid domain $[0, 0.2]$.
• Figure 5: Numerical solution in terms of pressure and velocity showing seven time instances from $t= 400 \mu s$ until $t =1000 \mu s$ over the computational domain with coupling interface at $x=0$, where the structure and the fluids interact.

Theorems & Definitions (3)

• Remark 3.1
• Remark 3.2
• Remark 4.2