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arxiv: 2410.22127 · v2 · submitted 2024-10-29 · ⚛️ physics.flu-dyn

Consistent Interface Capturing Adaptive Reconstruction Approach for Viscous Compressible Multicomponent Flows

Amareshwara Sainadh Chamarthi This is my paper

Pith reviewed 2026-05-23 19:27 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords multicomponent flowsinterface capturingTHINC reconstructioncontact discontinuity detectorviscous compressible flowsDucros sensornumerical discretization
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0 comments X

The pith

A discretization method applies THINC reconstruction only at detected contact discontinuities and central schemes to tangential velocities to capture material interfaces sharply in viscous multicomponent flows.

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

The paper develops a contact discontinuity detector that switches to the THINC reconstruction for phasic densities and volume fractions near material interfaces while using monotonicity-preserving or WENO schemes elsewhere. It further applies a central reconstruction scheme to tangential velocities across those interfaces, identified by the Ducros sensor, because those velocities remain continuous in viscous flows. The approach is shown to reduce dissipation errors at contacts without generating oscillations. Benchmark tests demonstrate that the combined scheme produces sharper interface representations than standard methods.

Core claim

The proposed discretization uses a contact discontinuity detector to apply the THINC reconstruction selectively to the contact wave, volume fractions, and phasic densities, while reconstructing tangential velocities with a central scheme wherever the Ducros sensor indicates a material interface; this combination is claimed to capture interfaces sharply without oscillations because tangential velocities are continuous across such interfaces in viscous flows.

What carries the argument

Contact discontinuity detector that triggers THINC reconstruction for entropy waves and phasic densities, paired with Ducros-sensor-driven central reconstruction for tangential velocities.

If this is right

  • Dissipation errors near contact discontinuities are reduced by limiting THINC reconstruction to the entropy wave and phasic densities.
  • No oscillations appear at material interfaces when tangential velocities are reconstructed centrally using the Ducros sensor.
  • Material interfaces are captured more sharply than with standard MP or WENO reconstructions alone in the benchmark tests performed.
  • The method remains stable for both inviscid and viscous compressible multicomponent flows in the reported cases.

Where Pith is reading between the lines

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

  • The same selective-reconstruction logic could be tested on three-dimensional unstructured grids to check whether interface sharpness is preserved under mesh irregularity.
  • If the Ducros sensor misses weak contacts in certain regimes, replacing it with a dedicated material-interface sensor might further improve robustness.

Load-bearing premise

That applying a central reconstruction scheme to tangential velocities across material interfaces identified by the Ducros sensor will produce no oscillations.

What would settle it

A viscous multicomponent flow simulation in which the central tangential-velocity reconstruction across a detected material interface generates visible oscillations or excessive smearing compared with existing interface-capturing schemes.

Figures

Figures reproduced from arXiv: 2410.22127 by Amareshwara Sainadh Chamarthi.

Figure 1
Figure 1. Figure 1: Numerical solution for multi-species shock tube 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 isolated contact test case using [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Numerical solution for multicomponent shock-density wave interaction using [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Density profiles obtained for Shu-Osher test case using Li and new sensors. Solid line: Reference solution; green stars: density with Li sensor; red circles: density with new sensor; cyan squares: location of Li sensor’s detection region and blue circles: location of new sensor’s detection region. The Li sensors’ detection of high-frequency regions as discontinuities required further attention. It has been… view at source ↗
Figure 5
Figure 5. Figure 5: The TENO discontinuity sensor from [61]. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Density profile for Shu-Osher test case with the proposed sensor using 200, 400 and 800 grid points and HY-THINC scheme: Figs. 6(a), 6(b) and 6(c). Red circles: HY-THINC; blue circles: Sensor location; and dashed line: Reference solution. • Chamarthi and Frankel [7] also made similar observations in the work that the limiting process should be avoided in the high-frequency region by conducting simulations … view at source ↗
Figure 3
Figure 3. Figure 3: Using density as the variable to detect the interface also failed with the current sensor, as shown in [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 7
Figure 7. Figure 7: Discontinuity detection locations in various papers from the literature [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Results of Huang et al. [64] using THINC with permission from Elsevier BV 2024, License number 5936770943086. [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Numerical solution (density contours) and sensor activation region for Isentropic vortex, Example 4.4. Example 4.5. Inviscid Taylor-Green Vortex (Inviscid case) In this example, the performance of the contact discontinuity sensor in solving the three-dimensional inviscid Taylor-Green vortex problem, a classical benchmark problem in computational fluid dynamics, is investigated. This test case is a disconti… view at source ↗
Figure 10
Figure 10. Figure 10: Normalised kinetic energy and enstrophy using HY-THINC and MP5 schemes for Example 4.5 on grid size of 64 [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Figures show z-vorticity contours of the considered schemes on a grid size of 1962 for µ = 1.0 × 10−4 , Example 4.6. (a) HY-THINC-D, Primitive variables [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: z-vorticity contours of the HY-THINC-D scheme with primitive variable reconstruction on a grid size of 1962 for µ = 1.0 × 10−4 and θ = 120, Example 4.6. For comparison, [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Figure is taken from Reference [67], where the simulations are computed on a grid size of 320 [PITH_FULL_IMAGE:figures/full_fig_p024_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Figures show z-vorticity contours of the considered schemes computed on a grid size of 3202 for µ = 3.0 × 10−5 and θ = 80, Example 4.6. It has been explained in [51] that computing tangential velocities using a central scheme will prevent unphysical vortices for this test case. In the later test cases, numerical examples will show that the tangential velocities can be computed using a central scheme, even… view at source ↗
Figure 15
Figure 15. Figure 15: Figures show initial condition and density gradient contours for grid sizes 512 [PITH_FULL_IMAGE:figures/full_fig_p025_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Figures show density gradient contours, contact discontinuity sensor locations in [PITH_FULL_IMAGE:figures/full_fig_p026_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Figures show density gradient contours and pressure contours overlayed on volume fractions, for Example 4.7, on a [PITH_FULL_IMAGE:figures/full_fig_p027_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Density gradient contours, vorticity contours, volume fraction contours and the sensor location at time t = 5 using the HY-THINC scheme, Example 4.8, on a grid resolution of 3584 × 1536 for inviscid simulation. Figs. 18(a) and 18(b) show the density gradient contours and vorticity contours, respectively. The results are similar and competitive compared to those obtained by the multi-resolution approach of… view at source ↗
Figure 19
Figure 19. Figure 19: Density gradient contours at time t = 5 using various schemes, Example 4.8, on a grid resolution of 1792 × 768 for inviscid simulation. Numerical Schlieren images at various time instances t = 0.2, 1.0, 3.0, 3.5, 4.0 and 5.0 are shown in [PITH_FULL_IMAGE:figures/full_fig_p029_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Numerical Schlieren images at various time instances [PITH_FULL_IMAGE:figures/full_fig_p030_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Density gradient contours and v velocity contours at time t = 5 using HY-THINC-D scheme, Example 4.8, on a grid resolution of 3584 × 1536 for viscous simulation. 30 [PITH_FULL_IMAGE:figures/full_fig_p030_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Figures show density gradient contours for characteristic variable reconstruction, density gradient contours for [PITH_FULL_IMAGE:figures/full_fig_p031_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Schematic of initial condition of Ricthmyer-Meshkov instability, Example 4.9. [PITH_FULL_IMAGE:figures/full_fig_p032_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Comparison of normalized density gradient magnitude, ϕ, contours for two-dimensional viscous Richtmeyer-Meshkov instability problem in Example 4.9 on a grid size of 4096 × 256 and 8192 × 512. Contours are from 1 to 1.7 at time t= 11.0 using the proposed scheme. Example 4.10. Shock wave interaction with a multi-material bubble (Inviscid case) In this test case, a Mach 6.0 shock wave in the air meets a cyli… view at source ↗
Figure 25
Figure 25. Figure 25: Numerical Schlieren images at times t = 5.0 × 10−3 , 1.0 × 10−2 , and 1.5 × 10−2 for the shock multiple bubble test case using HY-THINC scheme, Example 4.10, on a grid resolution of 8192 × 2048, as in [68]. (a) t = 2.0 × 10−2 (b) t = 2.0 × 10−2 [PITH_FULL_IMAGE:figures/full_fig_p034_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Numerical Schlieren images and corresponding Vorticity contours at [PITH_FULL_IMAGE:figures/full_fig_p034_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Numerical Schlieren images and corresponding Vorticity contours at [PITH_FULL_IMAGE:figures/full_fig_p035_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: z-vorticity contours of the considered schemes computed on a grid size of 1962 , Example 4.6 [PITH_FULL_IMAGE:figures/full_fig_p037_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: shows the density gradient contours, inviscid scenario, obtained by the WENO-Z and WENO-Z THINC scheme at t = 5 for Example 4.8. It can be observed that the WENO-Z-THINC scheme, [PITH_FULL_IMAGE:figures/full_fig_p037_29.png] view at source ↗
read the original abstract

The paper proposes a physically consistent numerical discretization approach for simulating viscous compressible multicomponent flows. It has two main contributions. First, a contact discontinuity (and material interface) detector is developed. In those regions of contact discontinuities, the THINC (Tangent of Hyperbola for INterface Capturing) approach is used for reconstructing appropriate variables (phasic densities). For other flow regions, the variables are reconstructed using the Monotonicity-preserving (MP) scheme (or Weighted essentially non-oscillatory scheme (WENO)). For reconstruction in the characteristic space, the THINC approach is used only for the contact (or entropy) wave and volume fractions and for the reconstruction of primitive variables, the THINC approach is used for phasic densities and volume fractions only, offering an effective solution for reducing dissipation errors near contact discontinuities. The second contribution is the development of an algorithm that uses a central reconstruction scheme for the tangential velocities, as they are continuous across material interfaces in viscous flows. In this regard, the Ducros sensor (a shock detector that cannot detect material interfaces) is employed to compute the tangential velocities using a central scheme across material interfaces. Using the central scheme does not produce any oscillations at the material interface. The proposed approach is thoroughly validated with several benchmark test cases for compressible multicomponent flows, highlighting its advantages. The numerical results of the benchmark tests show that the proposed method captured the material interface sharply compared to existing methods.

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

2 major / 1 minor

Summary. The manuscript proposes a numerical discretization for viscous compressible multicomponent flows with two contributions: (1) a contact-discontinuity detector that applies THINC reconstruction to phasic densities and volume fractions (and to the contact wave in characteristic space) while using MP or WENO elsewhere, and (2) a Ducros-sensor-triggered central reconstruction for tangential velocities across material interfaces, asserted to produce no oscillations because the sensor cannot detect interfaces. The method is claimed to be validated on several benchmark tests, with results showing sharper material-interface capture than existing methods.

Significance. If the central claims hold, the approach could reduce numerical dissipation at material interfaces in viscous multicomponent flows without introducing oscillations, which would be useful for high-fidelity simulations in aerodynamics and combustion. The algorithmic construction itself introduces no free parameters or circular definitions.

major comments (2)
  1. [Abstract] Abstract (second contribution): the assertion that 'Using the central scheme does not produce any oscillations at the material interface' is unsupported by any derivation, eigenvalue analysis, modified-equation argument, or isolated numerical test. No with/without comparison for the tangential-velocity treatment is described, nor is any oscillation metric (e.g., max |Δu_tang| across the interface) reported. If this claim does not hold, the stated advantage of the second contribution is lost.
  2. [Abstract] Abstract (validation statement): the claim that 'the numerical results of the benchmark tests show that the proposed method captured the material interface sharply compared to existing methods' supplies neither quantitative error norms, convergence rates, nor tabulated comparisons. Without these data the improvement cannot be evaluated and the central claim remains unverified.
minor comments (1)
  1. [Abstract] The abstract does not name the specific benchmark tests or the existing methods used for comparison, which would help readers assess the scope of the validation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed review. We address each major comment point-by-point below, indicating where revisions will be made to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract (second contribution): the assertion that 'Using the central scheme does not produce any oscillations at the material interface' is unsupported by any derivation, eigenvalue analysis, modified-equation argument, or isolated numerical test. No with/without comparison for the tangential-velocity treatment is described, nor is any oscillation metric (e.g., max |Δu_tang| across the interface) reported. If this claim does not hold, the stated advantage of the second contribution is lost.

    Authors: We agree that the abstract statement lacks explicit supporting analysis or tests in its current form. The physical basis is that tangential velocity is continuous across material interfaces for viscous flows, and the Ducros sensor (a shock detector) does not trigger at interfaces, so the central scheme is applied only where the velocity field remains smooth. To address the concern rigorously, we will add an isolated numerical test in the revised manuscript comparing tangential velocity profiles across an interface with and without the central scheme, including a quantitative oscillation metric such as max |Δu_tang|. A brief explanatory paragraph will also be inserted in the methods section. revision: yes

  2. Referee: [Abstract] Abstract (validation statement): the claim that 'the numerical results of the benchmark tests show that the proposed method captured the material interface sharply compared to existing methods' supplies neither quantitative error norms, convergence rates, nor tabulated comparisons. Without these data the improvement cannot be evaluated and the central claim remains unverified.

    Authors: We concur that quantitative metrics are necessary to substantiate the improvement claims. In the revised manuscript we will augment the validation section with L1 and L2 error norms for key variables (e.g., density and volume fraction), observed convergence rates on successively refined meshes, and tabulated side-by-side comparisons against the reference methods used in the benchmarks. These additions will allow direct, objective evaluation of the interface-capturing gains. revision: yes

Circularity Check

0 steps flagged

No circularity detected; derivation is an independent algorithmic construction

full rationale

The paper defines an algorithmic discretization that combines a contact-discontinuity detector with THINC reconstruction for phasic densities and volume fractions, MP/WENO elsewhere, and Ducros-triggered central reconstruction for tangential velocities. No equation or central claim reduces by construction to a fitted parameter, self-definition, or self-citation chain; the assertion that the central scheme produces no oscillations is presented as a design choice without supporting derivation, yet this does not create circularity because the result is not forced to equal its inputs. Benchmarks supply external empirical checks, rendering the method self-contained against the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper introduces algorithmic adaptations of existing reconstruction schemes rather than new physical entities or fitted constants; the main unstated premise is the oscillation-free behavior of the central tangential-velocity scheme.

axioms (1)
  • domain assumption Central reconstruction of tangential velocities across material interfaces identified by the Ducros sensor produces no oscillations
    Invoked in the description of the second contribution for viscous flows

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Reference graph

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