A simulation-derived surrogate model for the vaporization rate of aluminum droplets heated by a passing shock wave

Das, Pratik; Udaykumar, H. S.

doi:10.1016/j.ijmultiphaseflow.2020.103299

Cited by 8 publications

(2 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In governing equations for fluids, the effects other than convection and diffusion are usually described by source terms. Sources can exhibit singularities in some complex problems, such as surface tension [16,24], evaporation [10][11][12], phase transition [22,31,36,39], condensation [8], geometric constraints [9,33,35]. The singular source induces jumps in the state of flow and leads to new difficulties in the analysis of fluid motion.…”

Section: Introductionmentioning

confidence: 99%

Riemann problem of Euler equations with singular sources

Yu¹,

Liu²,

Feng³

2022

Preprint

View full text Add to dashboard Cite

This paper is concerned with the Riemann problem of one-dimensional Euler equations with a singular source. The exact solution of this Riemann problem contains a stationary discontinuity induced by the singular source, which is different from all the simple waves in the Riemann solution of classical Euler equations. We propose an eigenvalue-based monotonicity criterion to select the physical curve of this stationary discontinuity. By including this stationary discontinuity as an elementary wave, the structure of Riemann solution becomes diverse, e.g. the number of waves is not fixed and interactions between two waves become possible. Under the double CRP framework, we prove all possible structures of the Riemann solution.

show abstract

Section: Introductionmentioning

confidence: 99%

Riemann problem of Euler equations with singular sources

Yu¹,

Liu²,

Feng³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The governing equations for many mechanical problems involving fluids are hyperbolic conservation laws with singular sources. For example, surface tension [18,26], evaporation [15][16][17], phase transition [25,32,33,40,42,43] and condensation [11] at the interface of multiphase flows are formulated by singular sources. Geometric constraints on irregular domains can also 1 INTRODUCTION lead to the generation of singular sources in simplified governing equations, such as the shallow water equations with discontinuous river beds [19,35,39] and the governing equations of nozzle flow with discontinuous cross-section [13,44].…”

Section: Introductionmentioning

confidence: 99%

A well-balanced scheme for Euler equations with singular sources

Yu¹,

Liu²,

Feng³

2022

Preprint

View full text Add to dashboard Cite

Numerical methods for the Euler equations with a singular source are discussed in this paper. The stationary discontinuity induced by the singular source and its coupling with the convection of fluid presents challenges to numerical methods. We show that the splitting scheme is not well-balanced and leads to incorrect results; in addition, some popular well-balanced schemes also give incorrect solutions in extreme cases due to the singularity of source. To fix such difficulties, we propose a solution-structure based approximate Riemann solver, in which the structure of Riemann solution is first predicted and then its corresponding approximate solver is given. The proposed solver can be applied to the calculation of numerical fluxes in a general finite volume method, which can lead to a new well-balanced scheme.Numerical tests show that the discontinuous Galerkin method based on the present approximate Riemann solver has the ability to capture each wave accurately.

show abstract