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arxiv: 2606.17969 · v1 · pith:C47C54K6new · submitted 2026-06-16 · ⚛️ physics.comp-ph

High-Order Simulation of Particle-Laden Flows in Moving Domains Using Coupled ALE and Sliding Mesh Approaches

Anna Schwarz , Patrick Kopper This is my paper

Pith reviewed 2026-06-26 21:58 UTC · model grok-4.3

classification ⚛️ physics.comp-ph
keywords particle-laden flowsmoving domainsarbitrary Lagrangian-Euleriansliding meshdiscontinuous Galerkin spectral element methodLagrangian particle trackingmesh morphingcompressor rotor
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The pith

A coupled ALE and sliding mesh method tracks Lagrangian particles with strict spatial and temporal accuracy across non-conforming interfaces in moving domains.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a high-fidelity Euler-Lagrange framework that pairs a high-order discontinuous Galerkin spectral element method for the fluid with Lagrangian point-particle tracking. It handles moving geometries by combining arbitrary Lagrangian-Eulerian mesh deformation for general surface changes with a sliding mesh approach for rigid rotation or translation. Radial basis function morphing is embedded directly in the time-stepping procedure to account for the interaction between deforming surfaces and the flow. The central technical step enforces high-order accuracy for particles as they cross the non-matching grid boundaries between adjacent moving zones. The resulting scheme is demonstrated on benchmark cases and then used for particle erosion and wake interaction inside compressor rotors.

Core claim

The proposed algorithm resolves the sliding mesh tracking problem by enforcing strict spatial and temporal accuracy as Lagrangian particles cross non-conforming grid interfaces between adjacent moving zones.

What carries the argument

Radial basis function morphing integrated into the temporal evolution step of the ALE formulation, together with high-order coupling of the Lagrangian particle tracker to the sliding-mesh interfaces.

If this is right

  • Particle trajectories remain high-order accurate inside rotating machinery even when the mesh is partitioned into sliding zones.
  • The same time-stepping procedure can be used for both general deforming surfaces and rigid-body sliding motion without loss of formal accuracy.
  • Two-way coupled simulations of solid-particle erosion become feasible at high order in compressor rotor passages.
  • The framework extends directly to cases that combine upstream wake generators with downstream rotor blades.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same interface treatment could be applied to other non-conforming moving-boundary problems that do not involve particles.
  • If the radial-basis morphing step can be made cheaper, the method might become practical for long-time integration of many-particle systems.
  • The approach opens a route to systematic grid-convergence studies of particle statistics in full-stage turbomachinery.

Load-bearing premise

Radial basis function morphing can capture the non-linear feedback between changing surface shapes and the continuous phase while still preserving the high-order accuracy of the discontinuous Galerkin scheme.

What would settle it

A convergence study in which the observed order of accuracy for particle position or velocity drops below the design order precisely when particles cross a sliding-mesh interface.

Figures

Figures reproduced from arXiv: 2606.17969 by Anna Schwarz, Patrick Kopper.

Figure 1
Figure 1. Figure 1: Sketch of the particle-induced wall-deformation using RBFs to model [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Non-conforming element interface between a big element ( [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Flow chart of the DG operator for 4-way coupled particle-laden flow [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Particle path in the stationary (left) and relative (right) frame of ref [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Left: Normalized relative particle velocity for the Sod shock tube. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 8
Figure 8. Figure 8: Setup of the convergence test for curved faces. [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Experimental rate of convergence for p-refinement and h-refinement for continuous (left) and discrete (right) phase with the arbitrary Lagrangian– Eulerian approach on a nonconforming grid with two sliding mesh interfaces. vector ν = [0, 1, 0] ⊤ while the outer subdomains remain invari￾ant. Again, EOC for p-refinement and h-refinement are shown in fig. 9 (left) with the EOC confirming the expected spectral… view at source ↗
Figure 7
Figure 7. Figure 7: Experimental rate of convergence for t-convergence for the discrete phase with CFL = {0.0625 · 2 k : k ∈ N, k ∈ [0, 4]} and N = 6 (left) and h￾convergence for the discrete phase interacting with a moving curved face with Ngeo = N = 4 (right). Since only straight faces have been investigated so far, the accuracy of intersections of particles with moving curved faces is now evaluated. For this, a half circle… view at source ↗
Figure 10
Figure 10. Figure 10: Instantaneous flow field colored by the Mach number around the [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Probability distribution function (PDF) of particle impact and re e 0.6 e [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: Normalized, two-dimensional particle density distribution in the [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗
Figure 16
Figure 16. Figure 16: Mean and standard deviation σ, indicated by the root mean square (RMS), of the particle velocity against axial position normalized by the chord [PITH_FULL_IMAGE:figures/full_fig_p011_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Fluid velocity and particle flow rate upstream and downstream of [PITH_FULL_IMAGE:figures/full_fig_p011_17.png] view at source ↗
read the original abstract

In practical applications, compressible particle-laden flows in moving geometries involve complex, non-linear, and multi-scale inter-actions with turbulent structures. Resolving these dynamics numerically requires careful algorithmic treatment to accurately predict particle trajectories. This work presents a high-fidelity Euler-Lagrange framework that couples a high-order discontinuous Galerkin spectral element method for the continuous phase with a Lagrangian point-particle tracking scheme. To manage moving and deforming domains, the framework integrates two distinct mesh movement strategies: the arbitrary Lagrangian-Eulerian method for general mesh deformations such as time-resolved particle-induced surface deformations and its special interface case, the sliding mesh approach, uniquely suited for rigid rotational or translational movements. A primary focus is placed on tightly coupling the arbitrary Lagrangian-Eulerian formulation into the temporal evolution step by utilizing radial basis function morphing to capture the non-linear feedback loop between evolving surface topologies and the continuous phase. Concurrently, the framework ensures time- and high-order accurate coupling of the mesh movement algorithms with the dispersed phase. In particular, the proposed algorithm resolves the sliding mesh tracking problem by enforcing strict spatial and temporal accuracy as Lagrangian particles cross non-conforming grid interfaces between adjacent moving zones. The algorithms are rigorously validated against multiple benchmarks and subsequently applied to two challenging compressor rotor applications: the first focusing on solid-particle erosion, and the second featuring an upstream cylindrical wake generator.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript presents a high-fidelity Euler-Lagrange framework for compressible particle-laden flows in moving domains. It couples a discontinuous Galerkin spectral element method (DGSEM) for the continuous phase with Lagrangian point-particle tracking. Mesh movement is handled by the arbitrary Lagrangian-Eulerian (ALE) method with radial basis function (RBF) morphing for general deformations and a sliding mesh approach for rigid motions. Special emphasis is placed on maintaining high-order spatial and temporal accuracy for particles crossing non-conforming interfaces in the sliding mesh. The framework is validated against benchmarks and applied to two compressor rotor applications involving solid-particle erosion and upstream wake generators.

Significance. Should the high-order accuracy and coupling be rigorously demonstrated as claimed, this work would offer an important tool for simulating complex particle-laden flows in engineering applications like turbomachinery. The combination of ALE, RBF, and sliding mesh within a high-order DGSEM context addresses a challenging problem in computational fluid dynamics with potential for broader adoption in moving domain simulations. The explicit focus on particle tracking across sliding interfaces is a practical strength.

minor comments (3)
  1. The abstract refers to 'rigorous validation against multiple benchmarks' but does not list them or report error norms; a summary table of benchmarks, polynomial degrees, and observed convergence rates in the results section would strengthen the presentation.
  2. Notation for the RBF morphing parameters and their integration into the time-stepping scheme could be clarified with an explicit equation or pseudocode in the methods section describing the temporal evolution.
  3. Figure captions for the compressor rotor applications should include details on mesh resolution, particle counts, and time-step sizes to allow reproducibility assessment.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and the recommendation for minor revision. The referee summary accurately reflects the scope, methods, and applications presented in the work.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper describes an algorithmic framework for coupling high-order DGSEM with ALE mesh motion, sliding-mesh interfaces, RBF morphing, and Lagrangian particle tracking. All load-bearing steps are explicit constructions of the numerical scheme (interface-aware particle crossing, temporal integration of mesh motion, etc.) whose properties are asserted to follow from the chosen discretizations and are checked against external benchmarks. No equations reduce a claimed result to a fitted input by construction, no uniqueness theorem is imported from self-citation, and no ansatz is smuggled via prior work. The derivation chain is therefore the algorithm definition itself, which remains self-contained and externally falsifiable.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no information on free parameters, axioms, or invented entities.

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Works this paper leans on

54 extracted references · 30 canonical work pages

  1. [1]

    Ghenaiet, Study of Sand Particle Trajectories and Ero- sion Into the First Fan Stage of a Turbofan, in: V olume 7: Turbomachinery, Parts A, B, and C, ASMEDC, 2010, pp

    A. Ghenaiet, Study of Sand Particle Trajectories and Ero- sion Into the First Fan Stage of a Turbofan, in: V olume 7: Turbomachinery, Parts A, B, and C, ASMEDC, 2010, pp. 183–201. doi:10.1115/GT2010-22415

    work page doi:10.1115/gt2010-22415 2010

  2. [2]

    A. Beck, P. Ortwein, P. Kopper, N. Krais, D. Kempf, C. Koch, Towards high-fidelity erosion prediction: On time-accurate particle tracking in turbomachin- ery, International Journal of Heat and Fluid Flow 79 (2019) 108457. doi:10.1016/j.ijheatfluidflow. 2019.108457

    work page doi:10.1016/j.ijheatfluidflow 2019

  3. [3]

    Hartmann, M

    J. Hartmann, M. Lorenz, M. Klein, S. Staudacher, The Effect of an Entirely Eroded Airfoil on the Aerodynamic Performance of a Supersonic Compressor Cascade, in: V olume 10B: Turbomachinery — Axial Flow Turbine Aerodynamics; Deposition, Erosion, Fouling, and Icing; Radial Turbomachinery Aerodynamics, volume 81752, American Society of Mechanical Engineers, ...

    work page doi:10.1115/gt2022-81752 2022

  4. [4]

    Balachandar, J

    S. Balachandar, J. K. Eaton, Turbulent dispersed multiphase flow, Annual Review of Fluid Mechan- ics 42 (2010) 111–133. doi:10.1146/annurev.fluid. 010908.165243

    work page doi:10.1146/annurev.fluid 2010

  5. [5]

    E. J. Ching, M. Ihme, Development of a particle colli- sion algorithm for discontinuous Galerkin simulations of compressible multiphase flows, Journal of Computational Physics 436 (2021) 110319. doi:10.1016/j.jcp.2021. 110319

    work page doi:10.1016/j.jcp.2021 2021

  6. [6]

    Schwarz, P

    A. Schwarz, P. Kopper, E. de Staercke, A. Beck, Efficient computation of particle-fluid and particle-particle interac- tions in compressible flow, Computer Physics Communi- cations 315 (2025) 109743. doi:10.1016/j.cpc.2025. 109743

    work page doi:10.1016/j.cpc.2025 2025

  7. [7]

    C. A. A. Minoli, D. A. Kopriva, Discontinuous Galerkin spectral element approximations on moving meshes, Jour- nal of Computational Physics 230 (2011) 1876–1902. doi:10.1016/j.jcp.2010.11.038

    work page doi:10.1016/j.jcp.2010.11.038 2011

  8. [8]

    L. Wang, P. O. Persson, High-order discontinuous Galerkin simulations on moving domains using an ALE formulation and local remeshing with projections, 53rd AIAA Aerospace Sciences Meeting (2015) 1–12

    2015

  9. [9]

    Schwarz, J

    A. Schwarz, J. Keim, C. Rohde, A. Beck, Entropy sta- ble shock capturing for high-order DGSEM on mov- ing meshes, 2025. doi:10.48550/arXiv.2503.23237. arXiv:2503.23237

    work page doi:10.48550/arxiv.2503.23237 2025

  10. [10]

    M. J. Y ., Cfd simulation of flows in stirred tank reac- tors using a sliding mesh technique, Instn. Chem. Engng. Symp. Ser. 136 (1994) 341–348. 12

    1994

  11. [11]

    Dürrwächter, M

    J. Dürrwächter, M. Kurz, P. Kopper, D. Kempf, C.-D. Munz, A. Beck, An efficient sliding mesh interface method for high-order discontinuous Galerkin schemes, Computers & Fluids 217 (2021) 104825. doi:10.1016/ j.compfluid.2020.104825

    arXiv 2021

  12. [12]

    G. Wang, F. Duchaine, D. Papadogiannis, I. Duran, S. Moreau, L. Y . M. Gicquel, An overset grid method for large eddy simulation of turbomachinery stages, Journal of Computational Physics 274 (2014) 333–355. doi:10. 1016/j.jcp.2014.06.006

    2014

  13. [13]

    J. R. Aarnes, N. E. L. Haugen, H. I. Andersson, High- order overset grid method for detecting particle impaction on a cylinder in a cross flow, International Journal of Computational Fluid Dynamics 33 (2019) 43–58. doi:10. 1080/10618562.2019.1593385

    arXiv 2019

  14. [15]

    Lesoinne, C

    M. Lesoinne, C. Farhat, Geometric conservation laws for flow problems with moving boundaries and deformable meshes, and their impact on aeroelastic computations, Computer Methods in Applied Mechanics and Engineer- ing 134 (1996) 71–90. doi:10.1016/0045-7825(96) 01028-6

    work page doi:10.1016/0045-7825(96 1996

  15. [16]

    Krais, Moving Mesh Methods and Wall Modelling for Discontinuous Galerkin Schemes, Ph.D

    N. Krais, Moving Mesh Methods and Wall Modelling for Discontinuous Galerkin Schemes, Ph.D. thesis, Univer- sity of Stuttgart, 2020

    2020

  16. [17]

    C. Lo, J. P. Bons, Smoothing Techniques to Improve Flow Solution Convergence for Modeling Surface Erosion or Deposition in Two-Phase Flows, in: AIAA SCITECH 2023 Forum, American Institute of Aeronautics and As- tronautics, 2023. doi:10.2514/6.2023-1642

    work page doi:10.2514/6.2023-1642 2023

  17. [18]

    Y . Xiao, Y . Peng, P. J. Ming, W. M. Yang, A robust par- allel algorithm for Eulerian-Lagrangian method crossing sliding non-conformal interfaces, Computers & Fluids 264 (2023) 105974. doi:10.1016/j.compfluid.2023. 105974

    work page doi:10.1016/j.compfluid.2023 2023

  18. [19]

    Morelli, T

    M. Morelli, T. Bellosta, A. Guardone, Lagrangian Particle Tracking in Deforming Sliding Mesh for Rotorcraft Icing Applications, European Rotorcraft Forum (2019)

    2019

  19. [20]

    W. C. Maxon, T. Nielsen, N. Denissen, J. D. Regele, J. McFarland, A high resolution simulation of a single shock-accelerated particle, Journal of Fluids Engineering 143 (2021). doi:10.1115/1.4050007

    work page doi:10.1115/1.4050007 2021

  20. [21]

    Kopper, A

    P. Kopper, A. Schwarz, S. M. Copplestone, P. Ortwein, S. Staudacher, A. Beck, A framework for high-fidelity particle tracking on massively parallel systems, Computer Physics Communications 289 (2023) 108762. doi:10. 1016/j.cpc.2023.108762

    arXiv 2023

  21. [22]

    D. A. Kopriva, Metric identities and the discontinuous spectral element method on curvilinear meshes, J. of Sci. Comput. 26 (2006) 301

    2006

  22. [23]

    Schnücke, N

    G. Schnücke, N. Krais, T. Bolemann, G. J. Gassner, En- tropy Stable Discontinuous Galerkin Schemes on Moving Meshes for Hyperbolic Conservation Laws, J. Sci. Com- put. 82 (2020) 69. doi:10.1007/s10915-020-01171-7

    work page doi:10.1007/s10915-020-01171-7 2020

  23. [24]

    Sutherland, Lii

    W. Sutherland, Lii. the viscosity of gases and molecular force, The London, Edinburgh, and Dublin Philosophi- cal Magazine and Journal of Science 36 (1893) 507–531. doi:10.1080/14786449308620508

    work page doi:10.1080/14786449308620508

  24. [25]

    M. R. Maxey, J. J. Riley, Equation of motion for a small rigid sphere in a nonuniform flow, Physics of Fluids 26 (1983) 883–889. doi:10.1063/1.864230

    work page doi:10.1063/1.864230 1983

  25. [26]

    Gatignol, The Faxén formulae for a rigid particle in an unsteady non-uniform Stokes flow, Journal de Mecanique Theorique et Appliquee 2 (1983) 143–160

    R. Gatignol, The Faxén formulae for a rigid particle in an unsteady non-uniform Stokes flow, Journal de Mecanique Theorique et Appliquee 2 (1983) 143–160

    1983

  26. [27]

    E. Loth, J. T. Daspit, M. Jeong, T. Nagata, T. Nono- mura, Supersonic and hypersonic drag coefficients for a sphere, AIAA Journal 59 (2021) 3261–3274. doi:10. 2514/1.J060153

    2021

  27. [28]

    Schwarz, P

    A. Schwarz, P. Kopper, J. Keim, H. Sommerfeld, C. Koch, A. Beck, A neural network based framework to model particle rebound and fracture, Wear (2022) 204476. doi:10.1016/j.wear.2022.204476

    work page doi:10.1016/j.wear.2022.204476 2022

  28. [29]

    A. Uzi, A. Levy, On the relationship between erosion, energy dissipation and particle size, Wear 428-429 (2019) 404–416. doi:10.1016/j.wear.2019.04.006

    work page doi:10.1016/j.wear.2019.04.006 2019

  29. [30]

    Schwarz, High-Fidelity Particle Tracking and Impact- Induced Deformations, Ph.D

    A. Schwarz, High-Fidelity Particle Tracking and Impact- Induced Deformations, Ph.D. thesis, University of Stuttgart, 2024

    2024

  30. [31]

    Chandrashekar, Kinetic energy preserving and entropy stable finite volume schemes for compressible Euler and Navier-Stokes equations, Commun

    P. Chandrashekar, Kinetic energy preserving and entropy stable finite volume schemes for compressible Euler and Navier-Stokes equations, Commun. Comput. Phys. 14 (2013) 1252–1286

    2013

  31. [32]

    P. L. Roe, Approximate Riemann solvers, parame- ter vectors, and difference schemes, Journal of Com- putational Physics 43 (1981) 357–372. doi:10.1016/ 0021-9991(81)90128-5

    1981

  32. [33]

    Harten, J

    A. Harten, J. M. Hyman, Self adjusting grid methods for one-dimensional hyperbolic conservation laws, Jour- nal of Computational Physics 50 (1983) 235–269. doi:10. 1016/0021-9991(83)90066-9

    1983

  33. [34]

    Bassi, S

    F. Bassi, S. Rebay, A high-order accurate dis- continuous finite element method for the numeri- cal solution of the compressible Navier-Stokes equa- tions, Journal of Computational Physics 131 (1997) 267–279. URL:https://www.sciencedirect.com/ science/article/pii/S0021999196955722. doi:10. 1006/jcph.1996.5572. 13

    arXiv 1997

  34. [35]

    Hennemann, A

    S. Hennemann, A. M. Rueda-Ramírez, F. J. Hindenlang, G. J. Gassner, A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations, J. Comput. Phys. 426 (2021) 109935. doi:10.1016/j.jcp.2020.109935

    work page doi:10.1016/j.jcp.2020.109935 2021

  35. [36]

    M. H. Carpenter, a. Kennedy, Fourth-order Kutta schemes, Nasa Technical Memorandum 109112 (1994) 1–26

    1994

  36. [37]

    A. D. Beck, T. Bolemann, D. Flad, H. Frank, G. J. Gassner, F. Hindenlang, C.-D. Munz, High-order dis- continuous Galerkin spectral element methods for transi- tional and turbulent flow simulations, International Jour- nal for Numerical Methods in Fluids 76 (2014) 522–548. doi:10.1002/fld.3943

    work page doi:10.1002/fld.3943 2014

  37. [38]

    Krais, A

    N. Krais, A. Beck, T. Bolemann, H. Frank, D. Flad, G. Gassner, F. Hindenlang, M. Hoffmann, T. Kuhn, M. Sonntag, C.-D. Munz, FLEXI: A high order discon- tinuous Galerkin framework for hyperbolic-parabolic con- servation laws, Computers & Mathematics with Applica- tions 81 (2021) 186–219. doi:10.1016/j.camwa.2020. 05.004.arXiv:1910.02858

    work page doi:10.1016/j.camwa.2020 2021

  38. [39]

    Covering an ellipsoid with equal balls.Journal of Combinatorial Theory, Series A, 113(8):1667–1676, November 2006

    A. Schwarz, D. Kempf, J. Keim, P. Kopper, C. Rohde, A. Beck, Comparison of entropy stable collocation high- order DG methods for compressible turbulent flows, Com- puters & Fluids 303 (2025) 106874. doi:10.1016/j. compfluid.2025.106874

    work page doi:10.1016/j 2025

  39. [40]

    M. Kurz, D. Kempf, M. P. Blind, P. Kopper, P. Offen- häuser, A. Schwarz, S. Starr, J. Keim, A. Beck, GALÆXI: Solving complex compressible flows with high-order dis- continuous Galerkin methods on accelerator-based sys- tems, Computer Physics Communications 306 (2025) 109388. doi:10.1016/j.cpc.2024.109388

    work page doi:10.1016/j.cpc.2024.109388 2025

  40. [41]

    J. Keim, A. Schwarz, P. Kopper, M. Blind, C. Ro- hde, A. Beck, Entropy stable high-order discontinuous Galerkin spectral-element methods on curvilinear, hybrid meshes, Journal of Computational Physics 557 (2026) 114829. doi:10.1016/j.jcp.2026.114829

    work page doi:10.1016/j.jcp.2026.114829 2026

  41. [42]

    Mavriplis, Nonconforming discretizations and a poste- riori error estimators for adaptive spectral element tech- niques, Ph.D

    C. Mavriplis, Nonconforming discretizations and a poste- riori error estimators for adaptive spectral element tech- niques, Ph.D. thesis, Massachusetts Institute of Technol- ogy, 1989

    1989

  42. [43]

    D. A. Kopriva, A conservative staggered-grid Chebyshev multidomain method for compressible flows. II. A semi- structured method, Journal of Computational Physics 128 (1996) 475–488. doi:10.1006/jcph.1996.0225

    work page doi:10.1006/jcph.1996.0225 1996

  43. [44]

    D. A. Kopriva, A staggered-grid multidomain spectral method for the compressible Navier–Stokes equations, Journal of Computational Physics 143 (1998) 125–158. doi:10.1006/jcph.1998.5956

    work page doi:10.1006/jcph.1998.5956 1998

  44. [45]

    Morelli, T

    M. Morelli, T. Bellosta, A. Guardone, Efficient radial ba- sis function mesh deformation methods for aircraft icing, Journal of Computational and Applied Mathematics 392 (2021) 113492. doi:10.1016/j.cam.2021.113492

    work page doi:10.1016/j.cam.2021.113492 2021

  45. [46]

    Kopper, S

    P. Kopper, S. M. Copplestone, M. Pfeiffer, C. Koch, S. Fasoulas, A. Beck, Hybrid parallelization of Eu- ler–Lagrange simulations based on MPI-3 shared mem- ory, Advances in Engineering Software 174 (2022) 103291. doi:10.1016/j.advengsoft.2022.103291

    work page doi:10.1016/j.advengsoft.2022.103291 2022

  46. [47]

    Ortwein, S

    P. Ortwein, S. M. Copplestone, C.-D. Munz, T. Binder, W. Reschke, S. Fasoulas, A particle localization al- gorithm on unstructured curvilinear polynomial meshes, Computer Physics Communications 235 (2019) 63–74. doi:10.1016/j.cpc.2018.09.024

    work page doi:10.1016/j.cpc.2018.09.024 2019

  47. [48]

    Kopper, An Euler–Lagrange Method for Compressible Dispersed Multiscale Flow, Ph.D

    P. Kopper, An Euler–Lagrange Method for Compressible Dispersed Multiscale Flow, Ph.D. thesis, University of Stuttgart, 2024

    2024

  48. [49]

    Kopper, M

    P. Kopper, M. P. Blind, A. Schwarz, M. Kurz, F. Rodach, S. M. Copplestone, A. D. Beck, PyHOPE: A Python Toolkit for Three-Dimensional Unstructured High-Order Meshes, Journal of Open Source Software 10 (2025)

    2025

  49. [50]

    doi:10.21105/joss.08769

    work page doi:10.21105/joss.08769

  50. [51]

    Kaiser, D

    J. Kaiser, D. Appel, F. Fritz, S. Adami, N. Adams, A multiresolution local-timestepping scheme for particle- laden multiphase flow simulations using a level-set and point-particle approach, Computer Methods in Applied Mechanics and Engineering 384 (2021) 113966. doi:10. 1016/j.cma.2021.113966

    arXiv 2021

  51. [52]

    G. J. Gassner, F. Lörcher, C.-D. Munz, J. S. Hesthaven, Polymorphic nodal elements and their application in dis- continuous Galerkin methods, Journal of Computational Physics 228 (2009) 1573–1590. doi:10.1016/j.jcp. 2008.11.012

    work page doi:10.1016/j.jcp 2009

  52. [53]

    L. Reid, R. Moore, Design and overall performance of four highly loaded, high speed inlet stages for an advanced high-pressure-ratio core compressor, Technical Report, NASA-TP-1337, 1978

    1978

  53. [54]

    R. D. Moore, L. Reid, Performance of single-stage axial- flow transonic compressor with rotor and stator aspect ratios of 1.63 and 1.78, respectively, and with design pressure ratio of 1.82, Technical Report, NASA-TP-1338, 1978

    1978

  54. [55]

    Lorenz, M

    M. Lorenz, M. Klein, J. Hartmann, C. Koch, S. Stau- dacher, Prediction of Compressor Blade Erosion Experi- ments in a Cascade Based on Flat Plate Specimen, Fron- tiers in Mechanical Engineering 8 (2022) 1–14. doi:10. 3389/fmech.2022.925395. 14

    arXiv 2022