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arxiv: 2501.02416 · v1 · submitted 2025-01-05 · ⚛️ physics.flu-dyn · physics.comp-ph

Wave or Physics-Appropriate Multidimensional Upwinding Approach for Compressible Multiphase Flows

Amareshwara Sainadh Chamarthi This is my paper

Pith reviewed 2026-05-23 06:22 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn physics.comp-ph
keywords multidimensional upwindingmultiphase compressible flowsEuler equationscharacteristic reconstructionTHINC schemenumerical artifactsshock capturingvortical structures
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The pith

A new multidimensional upwinding method treats acoustic, vorticity, and entropy waves with separate reconstruction schemes to cut numerical artifacts in multiphase flows.

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

The paper introduces multidimensional algorithms that combine the wave structure of the Euler equations in characteristic space with physical-space properties for compressible multiphase flow simulation. Acoustic waves receive upwind reconstruction, vorticity and entropy waves receive central reconstruction, and material interfaces plus contact discontinuities receive THINC reconstruction; in physical space, phasic densities use THINC while tangential velocities use central schemes, with an adaptive switch to primitive variables near shocks identified via the stiffened gas parameter. The approach is shown to eliminate spurious vortices in shear layers, preserve vortical structures in gas-gas and gas-liquid cases, and improve shock-entropy interactions. A sympathetic reader would care because these changes produce visibly cleaner flow features and closer experimental agreement without adding extra dissipation or complexity to the base solver.

Core claim

The central claim is that applying upwind schemes to acoustic waves, central schemes to vorticity and entropy waves, and THINC reconstruction to interfaces and contacts in characteristic space, together with physical-space THINC on densities and central differencing on tangential velocities plus adaptive reconstruction using the stiffened gas parameter, yields higher accuracy, fewer numerical artifacts, and better experimental fidelity than conventional schemes across the tested multiphase cases.

What carries the argument

Characteristic decomposition of the Euler equations that isolates acoustic, vorticity, and entropy waves, each receiving a distinct reconstruction stencil (upwind for acoustic, central for vorticity/entropy, THINC for interfaces), augmented by physical-space THINC on phasic densities and an adaptive primitive/characteristic switch triggered by the stiffened gas parameter.

If this is right

  • Spurious vortices disappear from periodic shear-layer tests.
  • Vortical structures remain sharp in gas-gas and gas-liquid mixing problems.
  • Shock-entropy wave interactions show reduced post-shock oscillations and higher amplitude preservation.
  • Complex test cases match experimental data more closely than traditional one-dimensional upwinding schemes.

Where Pith is reading between the lines

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

  • The separation of wave families could be applied to other hyperbolic systems that admit a similar characteristic structure.
  • The adaptive switch between primitive and characteristic variables might reduce the need for special limiters near material interfaces in existing codes.
  • Extending the same wave-type logic to three-dimensional unstructured grids would test whether the artifact reduction persists when mesh topology changes.
  • The stiffened-gas identification step could be replaced by other phase indicators if the assumption that the parameter remains reliable near strong shocks proves fragile.

Load-bearing premise

The method assumes that the characteristic decomposition of the Euler equations continues to cleanly separate acoustic, vorticity, and entropy waves even in multiphase regions and that the stiffened gas parameter can correctly flag the liquid phase near discontinuities without misclassification or added error.

What would settle it

Running the standard shock-bubble interaction or gas-liquid Riemann problem with both the new scheme and a conventional MUSCL or WENO scheme and measuring whether the new scheme produces measurably lower spurious vorticity or closer agreement with the reference interface position and pressure trace.

Figures

Figures reproduced from arXiv: 2501.02416 by Amareshwara Sainadh Chamarthi.

Figure 1
Figure 1. Figure 1: Numerical solution for shock interface interaction problem in Example 4.1 on a grid size of [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Numerical solution for shock interface interaction problem in Example 4.1 on a grid size of [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Numerical solution for isolated contact test case using [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Numerical solution for Liquid-gas shock tube problem in Example 4.3 on a grid size of [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: z-vorticity contours on a grid size of 8002 , Example 4.4 [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: z-vorticity contours of the considered schemes on a grid size of 3202 , Example 4.4. (a) WENO5 (Prim). (b) MP5 (Prim). (c) Wave-MP (Prim) [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: z-vorticity contours of the considered schemes (using primitive variables) computed on a grid size of 3202 , Example 4.4 [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Figure is taken from Reference [48], where the simulations are computed on a grid size of 512 [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Figure shows the z-vorticity contours for the TENO, TENO-THINC and modified TENO-THINC (THINC for entropy wave only) schemes using a grid size of 3202 , Example 4.4. Example 4.5. Compressible triple point This test case examines the multi-species compressible triple-point problem, a two-dimensional Riemann problem involving three states and two distinct materials. The primary objective is to demonstrate th… view at source ↗
Figure 10
Figure 10. Figure 10: Density gradient contours at time t = 5 using various schemes, Example 4.5. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Figures 11(a) and 11(b) show sensor location regions. [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Density gradient contours at time t = 5 using primitive variable reconstruction schemes, Example 4.5. Example 4.6. 2D shock-entropy wave test This test case demonstrates the impact of reconstructing the entropy wave on the numerical solution. This test case is the two-dimensional shock-entropy wave interaction problem, modified for the multi-species case, proposed in [39] with the following initial condit… view at source ↗
Figure 13
Figure 13. Figure 13: The fine grid solution is shown in Figure 13(a) and coarse grid results computed using Wave-MP are shown in 13(b). [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Figure 14(a) shows the local density profiles for the MP5 and Wave-MP schemes, and Figure 14(b) shows the local [PITH_FULL_IMAGE:figures/full_fig_p024_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Volume fraction contours are shown in 15(a), Example 4.6. Figure 15(b) shows the local volume fraction at [PITH_FULL_IMAGE:figures/full_fig_p025_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Discontinuity detection locations from various papers using THINC from the literature. Figure 16(a) is reproduced [PITH_FULL_IMAGE:figures/full_fig_p026_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Cylindrical cavity collapse, Example 4.7, using Wave-MP approach. [PITH_FULL_IMAGE:figures/full_fig_p027_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Nonlinear function of normalized density gradient magnitude, [PITH_FULL_IMAGE:figures/full_fig_p028_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Nonlinear function of normalized density gradient magnitude, [PITH_FULL_IMAGE:figures/full_fig_p029_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Shock-water cylinder interation, Example 4.9, comparison of numerical results with experiment. [PITH_FULL_IMAGE:figures/full_fig_p030_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Shock-water cylinder interaction, Example 4.9. Numerical and experimental result at [PITH_FULL_IMAGE:figures/full_fig_p030_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Shock-water cylinder interaction, Example 4.9, on a 3072 [PITH_FULL_IMAGE:figures/full_fig_p031_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Shock-water cylinder interaction, Example 4.9, on a 3072 [PITH_FULL_IMAGE:figures/full_fig_p032_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Normalised kinetic energy and enstrophy using various schemes on grid size of 64 [PITH_FULL_IMAGE:figures/full_fig_p034_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Results from the literature. Figure 25(a) is reproduced from [41] with permission from Elsevier BV 2024, Li [PITH_FULL_IMAGE:figures/full_fig_p034_25.png] view at source ↗
read the original abstract

This paper introduces multidimensional algorithms for simulating multiphase flows, leveraging the wave structure of the Euler equations in characteristic space and the physical properties of variables in physical space. The algorithm applies different reconstruction schemes to acoustic, vorticity, and entropy waves in characteristic space to enhance accuracy and minimize numerical artifacts. In characteristic space, upwind schemes are used for acoustic waves, central schemes for vorticity and entropy waves, and Tangent of Hyper-bola for INterface Capturing (THINC) reconstruction for material interfaces and contact discontinuities (a subset of entropy waves). This approach prevents spurious vortices in periodic shear layers, accurately captures vortical structures in gas-gas and gas-liquid interactions, and improves the accuracy of shock-entropy wave interactions. In physical space, phasic densities are computed using THINC in regions of contact discontinuities and material interfaces, while tangential velocities are calculated with central schemes to improve vortical structures. An adaptive reconstruction technique is also introduced to mitigate oscillations near shocks, which arise from primitive variable reconstruction, by combining primitive and characteristic variable reconstructions with the liquid phase being identified using the stiffened gas parameter. The proposed multidimensional upwinding approach outperforms traditional schemes, demonstrating superior accuracy in capturing physical phenomena, reducing numerical artifacts, and better matching experimental results across complex test cases.

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

1 major / 0 minor

Summary. The paper introduces multidimensional upwinding algorithms for compressible multiphase flows that combine wave-structure decomposition in characteristic space (upwind schemes for acoustic waves, central schemes for vorticity and entropy waves, THINC for material interfaces) with physics-based reconstructions in physical space (THINC for phasic densities at contacts, central schemes for tangential velocities). An adaptive blend of primitive and characteristic variable reconstructions is proposed to suppress oscillations near shocks, with the liquid phase identified via the stiffened-gas parameter. The method is claimed to eliminate spurious vortices, improve vortical structure capture in gas-gas and gas-liquid interactions, and yield superior accuracy and experimental agreement relative to traditional schemes across complex test cases.

Significance. If the central claims hold after verification, the approach could reduce common numerical artifacts (spurious vorticity, interface oscillations) in multiphase compressible flow simulations without introducing additional free parameters. The use of standard wave decomposition and THINC reconstruction is a strength, but the absence of derivations, error analysis, or quantitative metrics in the abstract limits assessment of whether the gains are robust or merely case-specific.

major comments (1)
  1. [Abstract] Abstract (adaptive reconstruction paragraph): the central claim that the primitive-characteristic blend mitigates oscillations near shocks depends on the stiffened-gas parameter reliably flagging the liquid phase for stencil selection. Because this parameter varies continuously across numerically diffused interfaces, any threshold-based switch risks selecting the wrong reconstruction in cells with volume fractions between 0.1 and 0.9; the manuscript provides no validation or analysis of the identification logic in this transition regime, which directly undermines the oscillation-control assertion.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and the specific comment on the adaptive reconstruction description. We address the point directly below and will revise the manuscript accordingly to strengthen the presentation of the method.

read point-by-point responses

  1. Referee: [Abstract] Abstract (adaptive reconstruction paragraph): the central claim that the primitive-characteristic blend mitigates oscillations near shocks depends on the stiffened-gas parameter reliably flagging the liquid phase for stencil selection. Because this parameter varies continuously across numerically diffused interfaces, any threshold-based switch risks selecting the wrong reconstruction in cells with volume fractions between 0.1 and 0.9; the manuscript provides no validation or analysis of the identification logic in this transition regime, which directly undermines the oscillation-control assertion.

    Authors: We acknowledge that the current manuscript text does not include explicit validation or analysis of the stiffened-gas parameter threshold behavior across numerically diffused interfaces with intermediate volume fractions. The identification logic relies on the parameter value to select between primitive and characteristic reconstructions near shocks, but we agree that demonstrating its robustness in the 0.1–0.9 volume-fraction range would directly support the oscillation-mitigation claim. We will add a short subsection (or appendix) with supporting analysis, including the specific threshold criterion employed and results from representative interface-crossing cells, in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained from standard wave decomposition

full rationale

The paper constructs its multidimensional upwinding scheme directly from the characteristic decomposition of the Euler equations, applying established upwind/central/THINC reconstructions to acoustic, vorticity, and entropy waves plus an adaptive primitive-characteristic blend flagged by the stiffened-gas parameter. No equation or claim reduces by construction to a fitted parameter renamed as prediction, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled via prior work by the same authors. The algorithm is presented as a novel combination of existing techniques whose performance is then demonstrated on test cases; the derivation chain therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The approach rests on standard domain assumptions from hyperbolic PDE theory and CFD practice; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (3)
  • domain assumption The compressible Euler equations admit a characteristic decomposition separating acoustic, vorticity, and entropy waves.
    Invoked in the description of applying different schemes in characteristic space.
  • domain assumption THINC reconstruction preserves sharp material interfaces and contact discontinuities without excessive diffusion.
    Used for interfaces in both characteristic and physical space reconstructions.
  • domain assumption The stiffened gas equation of state parameter can identify the liquid phase for adaptive reconstruction decisions.
    Cited for mitigating oscillations near shocks via phase identification.

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Reference graph

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