Data of compressible multi-material flow simulations utilizing an efficient bimaterial Riemann problem solver

This paper presents fluid dynamics simulation data associated with two test cases in the related research article [1]. In this article, an efficient bimaterial Riemann problem solver is proposed to accelerate multi-material flow simulations that involve complex thermodynamic equations of state and strong discontinuities across material interfaces. The first test case is a one-dimensional benchmark problem, featuring large density jump (4 orders of magnitude) and drastically different thermodynamics relations across a material interface. The second test case simulates the nucleation of a pear-shaped vapor bubble induced by long-pulsed laser in water. This multiphysics simulation combines laser radiation, phase transition (vaporization), non-spherical bubble expansion, and the emission of acoustic and shock waves. Both test cases are performed using the M2C solver, which solves the three-dimensional Eulerian Navier-Stokes equations, utilizing the accelerated bimaterial Riemann solver. Source codes provided in this paper include the M2C solver and a standalone version of the accelerated Riemann problem solver. These source codes serve as references for researchers seeking to implement the acceleration algorithms introduced in the related research article. Simulation data provided include fluid pressure, velocity, density, laser radiance and bubble dynamics. The input files and the workflow to perform the simulations are also provided. These files, together with the source codes, allow researchers to replicate the simulation results presented in the research article, which can be a starting point for new research in laser-induced cavitation, bubble dynamics, and multiphase flow in general.


Multiphase flow Multi-material flow Riemann problem Equation of state Compressible flow a b s t r a c t
This paper presents fluid dynamics simulation data associated with two test cases in the related research article [1] .In this article, an efficient bimaterial Riemann problem solver is proposed to accelerate multi-material flow simulations that involve complex thermodynamic equations of state and strong discontinuities across material interfaces.The first test case is a one-dimensional benchmark problem, featuring large density jump (4 orders of magnitude) and drastically different thermodynamics relations across a material interface.The second test case simulates the nucleation of a pear-shaped vapor bubble induced by long-pulsed laser in water.This multiphysics simulation combines laser radiation, phase transition (vaporization), non-spherical bubble expansion, and the emission of acoustic and shock waves.Both test cases are performed using the M2C solver, which solves the three-dimensional Eulerian Navier-Stokes equations, utilizing the accelerated bimaterial Riemann solver.Source codes provided in this paper include the M2C solver and a standalone version of the accelerated Riemann problem solver.These source codes serve as references for researchers seeking to implement the acceleration algorithms introduced in the related research article.Simulation data provided include fluid pressure, velocity, density, laser radiance and bubble dynamics.The input files and the workflow to perform the simula-tions are also provided.These files, together with the source codes, allow researchers to replicate the simulation results presented in the research article, which can be a starting point for new research in laser-induced cavitation, bubble dynamics, and multiphase flow in general. ©

Value of the Data
• The data set in this paper come from two test cases in the related research article [1] , which develops an efficient bimaterial Riemann problem solver that significantly accelerates multimaterial flow simulations featuring arbitrary complex equations of state (EOS) and strong discontinuity across material interfaces.The associated source codes are provided to give researchers references to implement the acceleration algorithms introduced in the related research article.• The first test case is a one-dimensional benchmark problem, with a large density jump (4 orders of magnitude) and drastically different EOS across the material interface.This simulation provides a challenging test case for researchers who implement the acceleration algorithms in the related research article [1] , or who develop their own multi-material flow solution algorithms.• The second test case is about the nucleation and expansion of a pear-shaped bubble induced by a long-pulse laser.In laboratory experiments using the same type of laser, the same shape has been observed [3] .This simulation considers various realistic physical phenomena, including laser radiation, vaporization, non-spherical bubble expansion, and the emission of acoustic and shock waves.
• With the data and information provided in this paper, researchers can replicate the two simulations and use them as a starting point to study related problems involving bubble dynamics, laser-fluid interaction, vaporization, and multiphase flow.

Background
In compressible multi-material flow simulations, an unresolved challenge lies in computing advective fluxes across material interfaces that separate substantially different thermodynamic states and relations.A popular approach involves the local construction of Riemann problems and utilizing their exact solutions for flux computation.However, for complex equations of state, obtaining the exact solution of a Riemann problem proves computationally expensive due to the nested loops required.Multiplied by the large number of Riemann problems generated throughout a simulation, the resulting computational expenses are often prohibitive.In response to this challenge, the related research article [1] introduces a new Riemann problem solver designed to accelerate the solution of bimaterial Riemann problems without resorting to approximations or offline precomputation tasks.Consequently, the acceleration achieved by this new solver significantly enhances the performance of the advective flux calculator-a critical component akin to the engine of multi-material flow> solvers.Noteworthy speed gains, ranging from 18 to 81 times, were observed in various test cases, including underwater explosion, laser-induced cavitation, and hypervelocity impact.This data paper offers selected input and results files linked to two test cases in the original research article [1] .Complete source codes are also made available.The resource introduced here not only facilitates reproduction of the simulation results but also serves as a starting point for new research in bubble dynamics, vaporization, and multiphase flow in general.

Data Description
The data set in this paper is associated with two test cases in the related research article [1] , which significantly accelerates challenging multi-material flow simulations by developing a new, efficient bimaterial Riemann problem solver.Test 1 in this data paper is a one-dimensional (1D) benchmark problem, which models a condensed phase (soda lime glass) moving away from a gas (air) at a high speed (400 m/s).The density, velocity, and pressure distributions at t = 0 .15 μs are plotted in Fig. 1 .At any time t > 0 , the density ratio across the material interface reaches 4 orders of magnitude, from 0.3 kg/m 3 to 2203.98 kg/m 3 , which challenges the robustness of multi-material flow solvers.The simulation result data are generated using the high-fidelity multiphase computational fluid dynamics solver M2C [4] , which utilizes the accelerated bimaterial Riemann solver at material interfaces.The exact solution is generated using a standalone version of the efficient bimaterial Riemann problem solver [5] .The source codes of these two solvers are provided in the online data repository [2] (see Table 1 ).The file paths are relative to the main directory, i.e., the EfficientRiemann_DataSet folder in the online repository.
In the online data repository, Test 1 files are listed in Table 2 , including both the necessary input files for launching the simulation and selected simulation outputs.Again, the file paths   are expressed relative to the main directory, i.e., the EfficientRiemann_DataSet folder in online repository.Specifically, the Image.zipfile includes the subfigures in Fig. 1 .
Test 2 in this data paper simulates a pear-shaped bubble induced by a long-pulse laser.The simulation generates a variety of output data, including but not limited to laser radiance, fluid pressure, velocity, temperature, and level-set information used for tracking liquid-gas interfaces.Fig. 2 showcases a series of images that depict the evolution of laser radiance fields and the formation of a non-spherical bubble.Each sub-figure corresponds to a specific time instant, as indicated at the bottom.In Fig. 3 , a sequence of images illustrates the progression of pressure fields and the expansion of the pear-shaped bubble.More detailed numerical experiment setup,

Table 3
Simulation input and output files of Test2, laser-induced cavitation.

File path File description
LaserBubble/Simulation/input.st Input parameters LaserBubble/Simulation/Laser_power.txt The temporal profile of laser power (input) LaserBubble/Simulation/tinkercliffs_sbatch.sh The bash script for submitting the simulation on Tinkercliffs LaserBubble/Simulation/log.out The screen outputs generated by the simulation LaserBubble/ Simulation/meshinfo.txt Mesh information (output) LaserBubble/Images.zipImages generated using the simulation results LaserBubble/Videos/radiance_velocity.aviAn animation of the laser radiance and the velocity fields LaserBubble/Videos/pressure.aviAn animation of the pressure filed such as geometry of the laser radiation domain, spatial profile of laser radiance, and the temporal profile of laser power, can be found in [6] .Table 3 lists the files associated with Test 2 in the online data repository.Again, the file paths are expressed relative to the main directory.The files include input files that are necessary for launching the simulations and selected simulation outputs.In the file Images.zip, 1002 images are included to show the progression of the bubble dynamics, as well as the velocity,pressure, and laser radiance fields.Two animations created using these images are placed in the Videos folder.A file of mesh information is also outputted and placed in the Simulation folder.

Test2: laser-induced cavitation
In Table 4 , the characteristics of the laser are detailed.Table 5 outlines the properties of liquid water.Additionally, Table 6 provides the physical attributes of the water vapor confined within the bubble.
The modeling of liquid water employs the stiffened gas equation of state (EOS) [7] , characterized by γ = 6 .12 and p c = 343 MPa.These two parameters are determined as fitting parameters using shockwave Hugoniot data for water [8] .Meanwhile, the representation of water vapor is based on the perfect gas EOS.

Solver and external libraries
The multi-material flow simulations were performed using the M2C solver.The exact solution in Test 1 was generated by a standalone Riemann solver.These two solvers are uploaded to the online data repository, see Table 1 .Readers can also access these two solvers on GitHub [4] .The versions of external libraries used by these two solvers are listed in Table 7 .

Simulation process
For every multi-material flow test case, the simulation parameters are defined within the file input.st; Specifically for Test 2, the temporal profile of laser power is specified in laser_power.txt .The simulations were launched on the Tinkercliffs computer cluster at Virginia Tech, using their respective sbatch script tinkercliffs_sbatch.sh .
In Test 1, the simulation is carried out on a one-dimensional mesh with 200 elements.The time step size was around 0.95 ns.After 158 time steps ( t = 0 .15 μs ), the simulation was terminated.
In Test 2, we conduct the simulation on a two-dimensional mesh, taking advantage of the problem's cylindrical symmetry.The fluid mesh contains around 338, 0 0 0 finite volume cells.Throughout the simulation, the computational domain is divided into 256 subdomains, with each one assigned to one CPU core.The time step size ranged between 0.2 and 0.5 ns.After completing 369,817 time steps, which is equivalent to t = 50 μs , the simulation was successfully terminated.

Ethics Statement
The authors have read and follow the ethical requirements for publication in Data in Brief and confirm that the current work does not involve human subjects, animal experiments, or any data collected from social media platforms.
2024 The Authors.Published by Elsevier Inc.

Table 1
Source codes used to generate the results data.

Table 2
Simulation input and output files of Test1, 1D benchmark problem.Simulation/input_standaloneRiemann.stInput parameters for the standalone Riemann solver

Table 7
External libraries used by M2C.