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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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