parDG swMATH ID: 18743 Software Authors: Diehl, Dennis Description: Higher-order schemes for simulation of compressible liquid-vapor flows with phase change. With CD-ROM. The aim of this thesis is the numerical simulation of two-phase flows undergoing dynamical phase transitions. Such flows are of highly industrial interest since collapsing cavitation bubbles are responsible for erosion damage on ship propellers, pumps and turbines. Lord Rayleigh recognized in 1917 that collapsing vapor bubbles can cause this kind of damage. In this work the flow is modeled by the Navier-Stokes-Korteweg equations which belong to the class of Diffuse-Interface models. We develop efficient and reliable numerical schemes based on modern numerical techniques such as higher order Discontinuous Galerkin schemes, local mesh adaption, parallelization and load-balancing in multiple space dimensions. We provide a software package (written in C++) for the discretization of general time dependent partial differential equations. The discretization of the Navier-Stokes-Korteweg model is done on the basis of this package. For the validation of the resulting schemes special (quasi-exact) solutions are constructed. Several benchmarks show the efficiency and reliability of the methods. However, physical experiments are not available on the length scale that can be simulated and therefore the results cannot compared to real world data. Homepage: https://freidok.uni-freiburg.de/fedora/objects/freidok:3762/datastreams/FILE1/content Keywords: discontinuous Galerkin method; explicit Runge-Kutta scheme; Navier-Stokes-Korteweg model; C++ software package Related Software: FLEXI; HE-E1GODF; PETSc; ParMETIS; PolyMesher; PETSc/TS; NLIGA; PetIGA; FEniCS; RODAS; DOLFIN; ISTL; UG; FLENS; deal.ii; DUNE-FEM; DUNE; ALBERTA; UMFPACK; rbMIT Cited in: 23 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Higher-order schemes for simulation of compressible liquid-vapor flows with phase change. With CD-ROM. Zbl 1161.76002Diehl, Dennis 2007 all top 5 Cited by 56 Authors 5 Gómez, Héctor J. 3 Giesselmann, Jan 3 Rohde, Christian 3 Tian, Lulu 2 Bueno, Jesus 2 Diehl, Dennis 2 Fernandino, Maria 2 Gerritsma, Marc I. 2 Hughes, Thomas J. R. 2 Keim, Jens 2 Kraus, Christiane 2 Kröner, Dietmar 2 Kuerten, J. G. M. 2 Munz, Claus-Dieter 2 Nogueira, Xesús 2 Park, Keunsoo 2 Pryer, Tristan 2 van der Vegt, Jaap J. W. 2 Xu, Yan 1 Aki, Gonca L. 1 Bazilevs, Yuri 1 Bona-Casas, Carles 1 Calo, Victor Manuel 1 Chen, Zhangxin 1 Chertock, Alina E. 1 Daube, Johannes 1 Dedner, Andreas S. 1 Degond, Pierre 1 Dorao, Carlos A. 1 Dreyer, Wolfgang 1 Evans, John A. 1 Gao, Yali 1 Guo, Hui 1 Heida, Martin 1 Hermsdörfer, Katharina 1 Hitz, Timon 1 Hu, Tianyi 1 Jia, Rui 1 Khelladi, Sofiane 1 Klöfkorn, Robert 1 Kränkel, Mirko 1 Kremser, Jenny 1 Landis, Chad M. 1 Leng, Yu 1 Li, Rui 1 Liu, Ju 1 Makridakis, Charalambos G. 1 Málek, Josef 1 Martínez, Abel 1 Navarrina, Fermín 1 Neusser, Jochen 1 Nolte, Martin 1 Ohlberger, Mario 1 Ramirez, Luis J. 1 Souček, Ondřej 1 Yang, Yang all top 5 Cited in 13 Serials 7 Journal of Computational Physics 3 Computers & Mathematics with Applications 2 Computer Methods in Applied Mechanics and Engineering 1 International Journal of Engineering Science 1 Mathematics of Computation 1 Applied Mathematics and Computation 1 BIT 1 Computing 1 Computational Mechanics 1 Journal of Scientific Computing 1 Numerical Algorithms 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Interfaces and Free Boundaries all top 5 Cited in 8 Fields 19 Fluid mechanics (76-XX) 15 Numerical analysis (65-XX) 6 Partial differential equations (35-XX) 3 Mechanics of deformable solids (74-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Differential geometry (53-XX) 1 Computer science (68-XX) Citations by Year