Searcharxiv⌕ Search

arXiv subjects

Sai Peng

Publications and source records attributed to Sai Peng.

17 recordsLinked to original sources
arXiv2026

Projection-Lift Equivalence and Dissipation-Tight Compactness for Continuum-State FENE-Markov Fluids

We consider incompressible FENE dumbbells coupled to a reversible Markov operator on a compact continuum of internal states. At zero centre-of-mass diffusion we prove that state averaging is an exact factor map and that a Lagrangian state lift is its unique inverse on the natural energy-solution classes. Thus existence, multiplicity, and uniqueness of the state-resolved system are precisely those of its scalar FENE projection; the internal-state dynamics creates no additional large-data nonuniqueness. The lift is driven by a trace-free matrix fibre evolution and permits nonlinear local activities, including rates with linear dependence on the singular Kramers stress.We also prove a sequential form of this structure. For state-resolved regularizations with relative-entropy-prepared initial fibres and no viscous dissipation defect, the complete densities converge strongly without reconstructing them after the scalar limit. Consequently the full drag,state-dependent activity, singular stress, and non-atomic Jeffreys production all pass to the limit. The argument combines stability of regular Lagrangian flows with a relative-entropy estimate for simultaneously varying matrix drifts and jump rates. A stationary oscillation shows that the preparation cannot follow from the natural entropy bounds alone. With positive centre-of-mass diffusion we independently construct global large-data weak solutions and identify the same nonlinear terms. An explicit infinite-rank kernel proves that these results are not finite-species reductions.

math.AP↗
arXiv2026

Hopf Obstruction and Transported Forced Brakke Motion in Ordered Viscoelastic Cores

We study topological relaxation in ordered viscoelastic conformation flows at finite epsilon. In an ordered region, a positive spectral gap selects an oriented principal axis and hence an S^2-valued director with a Hopf class. We show that a change of this class must be accompanied, before the sharp-interface limit, by one of a finite list of costs: exterior gap concentration, ordered-core mass, boundary flux, FENE/collar loss, or a topology exit. The result is proved for a concrete Landau-de Gennes ordered-core closure coupled to an Oldroyd/FENE-type transport law. The structural hypotheses used in the argument are verified up to the first typed exit time: the Morse-Bott ordered well, tubular soft coordinates, massive-mode coercivity, a projected transported Ginzburg-Landau equation, exterior gap control, and tame FENE/collar coefficients. The projected Ginzburg-Landau equation separates translation modes from the remaining residuals. The translation modes give the normal line force, while the orthogonal soft, massive, geometric, and collar terms are absorbed by coercivity or charged to the corresponding exit. A modulated-energy argument propagates a nonempty class of vortex-tube data on regular intervals. On each such interval, the normalized core measures converge to an integral one-varifold satisfying a transported forced Brakke inequality with the computed force. The theorem therefore derives the force projection, open-basin propagation, and Brakke compactness estimates before invoking any limiting Brakke flow, and it records the finite-epsilon cost when the regular ordered-core description breaks down.

math.AP↗
arXiv2026

Arbitrary-Size Global Regularity for a Reduced Oldroyd-B Active-Line Model

We study a one-dimensional active-line equation motivated by thin stress-sheet dynamics in the high-Weissenberg Oldroyd-B regime. A positive periodic line density $\rho=m+\eta$ satisfies $\rho_t+cP_0\{\rho\Lambda\rho-(\mathcal H\rho)\rho_s\}+\gamma(\rho-m)=0$, where $\Lambda=\mathcal H\partial_s$ and $P_0f=f-\langle f\rangle$. We prove that every strictly positive smooth initial density of arbitrary size generates a unique global smooth solution. The key is the pointwise cancellation obtained after one differentiation: for $w=\rho_s$, $w_t+c\rho\Lambda w-c(\mathcal H\rho)w_s+\gamma w=0$. Its maximum principle controls the slope globally, while critical-drift H\"older and Schauder estimates close all higher derivatives. We also prove quantitative small-oscillation stability. Independently, an exact fourth-difference sum-of-squares identity gives $\int_{\mathbb T}\rho^2\Lambda^3\rho\,ds\geq0$ for every smooth nonnegative density. The stronger derivative-energy sign leads, in its sharp phase-opposed form, to the cubic convolution inequality $\mathcal C(x)\leq2AE_3$, where $A=\sum_{n\geq1}x_n$, $E_3=\sum_{n\geq1}n^3x_n^2$, and $\mathcal C(x)=\sum_{a,b\geq1}(a+b)(a^2+ab+b^2)x_ax_bx_{a+b}$. The constant $2$ is sharp along critical $n^{-3/2}$ plateaux. We prove the inequality for several cutoff-uniform and infinite-support classes, including selected Schur, dyadic-layer, Mellin, and moment families. The unrestricted inequality remains open, but it is not needed for the global regularity theorem.

math.AP↗
arXiv2026

Pressure Quotients and Endpoint Velocity-Clock Criteria for Non-Diffusive Viscoelastic Flows

We prove endpoint continuation criteria for stress-diffusion-free incompressible viscoelastic flows by working modulo pressure. In two space dimensions, the pressure-free part of any smooth spectral isotropic stress reduces to a single active deviatoric channel (q_1(a,|Y|^2)Y), where (C=aI+Y) and (\operatorname{tr}Y=0). This scalar quotient structure allows a weighted active-deviatoric energy to cancel the top-order coupling between polymer stretching and the divergence of the active stress. On compact conformation windows the resulting high-order estimate depends only on an endpoint velocity clock and a logarithmic conformation norm. For Oldroyd--B this gives continuation of strong two-dimensional solutions under (\nabla u\in L^1_tB^0_{\infty,1}), while for FENE-P it gives continuation under (\nabla u\in L^2_tB^0_{\infty,1}). In both models the compact conformation window and logarithmic bound are derived from the velocity clock and the model barriers, rather than imposed as independent hypotheses. The criteria are formulated in integer Sobolev strong-solution classes and do not assert Leray-type weak-solution or critical-space local well-posedness results. We also identify a static operator obstruction showing the functional necessity of the logarithmic threshold for the pressure-free stress map. In three dimensions the quotient contains an additional residual channel (q_2(Y^2)^\circ), so the exact scalar closure is intrinsically two-dimensional. On prescribed compact windows this residual can be absorbed by viscosity; for Oldroyd--B and FENE-P it vanishes because (q_2\equiv0).

math.AP↗
arXiv2026

Residual-Work Compatibility Criteria and Defect-Measure Compactness for Positive-Cone Viscoelastic Reynolds States

We prove a residual-work compatibility theory for positive-cone viscoelastic Reynolds states. In Oldroyd--B, the entropy cancellation eliminates incompressible transport and upper-convected stretching against polymeric stress work. After quotienting pressure tensors and spatial means, positive pressure-free residual work can be paid only by the conformation residual through the entropy-dual lever (G=I-A^{-1}). This yields the closed residual-work cone (P+(\alpha/2)\int_{\mathbb T^d}G:S,dx\le 0), exact windowed tests, and the least-cost Hilbert-space repair; constrained closures pay through the projected lever. Strong residual-data limits preserve this cone, while weak--weak limits require the product-defect measure carried by (G:S). The augmented topology is sharp, as shown by localized residual packets. For FENE-P, the lever (G_b(C)=((b-d)/(b-\operatorname{tr}C))I-C^{-1}) makes the finite-extensibility boundary a genuine residual-work boundary.

math.AP↗
arXiv2026

Three-Dimensional Positive-Cone Oldroyd-B Flows:Geometric Continuation and Residual-Work Criteria

We prove a three-dimensional positive-cone continuation criterion for the stress-diffusion-free Oldroyd-B system on the periodic torus. Writing the positive conformation tensor as A = exp(B), we show that finite-time breakdown of a strong H^s solution, s > 5/2, can occur only through loss of the logarithmic spectral envelope of A or divergence of the endpoint vorticity clock given by the time integral of the B^0_{infty,1} norm of curl u. The proof combines compact positive-cone envelopes, endpoint Biot-Savart estimates, and high-order logarithmic conformation estimates, without using stress diffusion. We also derive a positive-cone Reynolds admissibility criterion with an exact residual-work cost. The least L^2 conformation residual needed to pay positive pressure-free residual work is determined by the entropy-dual lever G = I - A^{-1}, and this cost degenerates quantitatively near the equilibrium A = I. Together, the two criteria identify the same positive-cone obstruction in the strong and relaxed regimes: before breakdown one must control the endpoint flow clock on a compact logarithmic cone, while after passage to a relaxed description positive residual work must be paid for by an exact entropy-dual conformation defect.

math.AP↗
arXiv2026

Entropy-Compatible Reconstruction for High-Weissenberg Viscoelastic Flow

Log-conformation and square-root reconstructions preserve positive definiteness in high-Weissenberg viscoelastic simulations, but positivity alone does not guarantee compatibility with the discrete free-energy balance. We identify three reconstruction-level mechanisms by which strictly positive tensors can still generate nonphysical behavior: Jensen-type entropy bias, exponential amplification of logarithmic perturbations in highly stretched states, and sign-indefinite polymeric-work defects caused by using incompatible tensors in stress work and entropy variables. We formulate an entropy-compatible reconstruction principle and a corrected logarithmic reconstruction selected by a least-damping entropy constraint. The correction is local, positive, computable by bisection, spectrally controlled, and compatible with coupled velocity--pressure--conformation time stepping. We prove existence of the maximal admissible parameter, convexity of the entropy profile along the logarithmic path, a compatible free-energy estimate, a defect-budget estimate for noncompatible reconstructions, asymptotic inactivity on high-order admissible defects, and a conditional high-stretch resolution advantage in log-relative and entropy metrics. Reproducible diagnostics compare logarithmic, square-root, and linear reconstructions and verify the predicted entropy defects, work defects, stress-force errors, and high-Weissenberg accumulation.

cond-mat.soft↗
arXiv2026

Entropy-Compatible Barrier Schemes for Diffusive FENE Flows

FENE-type conformation-tensor models impose a finite-extensibility constraint that is absent from Oldroyd--B flow: the conformation tensor must satisfy $\CC\succ0$ and $\tr\CC<L^2$. Positive definiteness alone is therefore insufficient, since a numerical state can remain positive while crossing the singular trace barrier. Even a trace-preserving logarithmic parametrization is not enough by itself: high-order reconstruction can remain inside the finite-extensibility domain while injecting artificial FENE entropy. We develop and analyze a barrier-preserving entropy-compatible discretization for FENE-P type flows with polymer center-of-mass molecular diffusion and for trace-singular FENE-family closures with the same entropy structure. The method combines a trace-barrier free energy, a finite-extensibility logarithmic parametrization, a least-damping entropy-compatible barrier-log reconstruction, molecular diffusion paired with the barrier entropy variable, compatible quadrature for polymeric work, and a scaled FENE stress variable for the small-Weissenberg limit. For admissible discrete states we prove finite-extensibility preservation at entropy quadrature points, existence and bisection computability of the maximal entropy-admissible reconstruction parameter, a fully discrete free-energy inequality with relaxation and molecular-diffusion barrier dissipation, a quantitative AP stress closure, and a fixed-discretization Newtonian limit. A conditional relative-entropy estimate is derived on compact subsets of the finite-extensibility domain. Numerical diagnostics verify barrier preservation, entropy-compatible reconstruction, energy decay, AP closure, coupled velocity--pressure--stress accuracy, and high-Weissenberg robustness near the trace constraint.

math.NA↗
arXiv2024

Vortex shedding and heat transfer from a heated circular cylinder in Bingham plastic fluids

The present study numerically investigates the vortex shedding and heat transfer characteristics of a heated circular cylinder immersed in Bingham plastic fluids.The effects of three parameters, i.e., (i) plastic Reynolds number ($10 \leq Re \leq 180$), (ii) Prandtl number ($1\leq Pr \leq 100$), and (iii) the Bingham number ($0 \leq Bn \leq 10,000$), are evaluated. The Navier-Stokes and energy equations for flow and heat transfer are adopted, along with the incorporation of the Papanastasiou regularization to address the discontinuous-viscosity characteristics of Bingham plastic fluids. To illustrate the impact of fluid yield stress on the flow structure, the study provides comprehensive insights into flow transition, streamlines, shear rate and velocity distributions, the morphology of yielded/unyielded regions, and the drag coefficient ($C_d$). Additionally, the temperature distribution, the local Nusselt number ($\overline{Nu_{local}}$) along the cylinder, and the average Nusselt number on the cylinder ($\overline{Nu}$) are analyzed. The results indicate that the flow transition of Bingham fluids over a circular cylinder is dependent on external disturbances, exhibiting subcritical bifurcation behavior. This leads to abrupt jumps in the $\overline{Cd}$ - $Bn$ curve and the $\overline{Nu}$ - $Bn$ curve near the critical Bingham number $Bn_c$. Furthermore, the heat transfer performance is contingent upon the different distribution of shear strain rate in the boundary layer across various $Bn$ ranges. It is observed that $\overline{Nu}$ and $Bn$ fits well with the Carreau-Yasuda-like non-Newtonian viscosity model. This investigation enhances the understanding of the vortex shedding and heat transfer behaviors in Bingham plastic fluids.

physics.flu-dyn↗
arXiv2024

Equivalent slip length of flow around a super-hydrophobic cylinder

In this research, a two-dimensional numerical simulation is conducted to determine the equivalent wall slip length for flow around a circular cylinder featuring a super-hydrophobic surface. The super-hydrophobic surface is modeled as an alternating distribution of slip and no-slip conditions along the cylinder's surface. The smallest unit of this alternating pattern is referred to as a monomer. The study takes into account the Reynolds number and two critical dimensionless parameters: the gas fraction (GF) and the ratio l/a. GF indicates the proportion of the slip length relative to the total length of the monomer, while l/a denotes the ratio of the monomer length (l) to the cylinder's radius (a). The ranges considered for the Reynolds number, GF, and l/a are from 0.2 to 180, 0.1 to 0.99, and $\pi$/80 to $\pi$/5, respectively. A dimensionless number, the Knudsen number (Kn), is introduced to measure the ratio between the equivalent slip length ($\lambda$) and the cylinder's diameter (D). By equating the integral wall friction resistance on the cylinder surface, a quantitative relationship between the equivalent Kn and the parameters (Re, GF, l/a) is established. A meticulous comparison of flow parameters between the equivalent slip length model and the slip-no-slip scenario reveals that the slip length model is an effective approximation for the slip-no-slip alternating model.

physics.flu-dyn↗
arXiv2022

Comparison of three numerical stabilization techniques of viscoelastic flows: vortex shedding behind a confined cylinder

In this study, the OpenFOAM platform, based on the finite volume method, is applied to investigate the two-dimensional viscoelastic flow past a circular cylinder. The FENE-P model, which considers the bounded elongation of polymer molecules, is chosen to describe the elastic constitutive relationship of the polymer solution. The maximum molecular chain lengths of L = 10, 50, 100, and 200 are considered, which describe the molecular conformation characteristics of the polymer solution. To improve the numerical instability of the viscoelastic flow simulation, three different methods, i.e., the traditional method (Td) with the addition of artificial viscosity, the logarithmic reconstruction method (Log), and the square root tensor method (Sqrt), are evaluated. The results show that the artificial viscosity has a little effect on the accuracy for the simulation with a small molecular chain length (L = 10). However, for long molecular chain lengths such as L = 100 and L = 200, the addition of artificial dissipation tends to overestimate the drag, which indicates that special caution is needed to incorporate the artificial dissipation in the simulation. Moreover, the logarithmic reconstruction method shows a strong grid-dependent characteristics, which may produce unphysical results.

physics.flu-dyn↗
arXiv2022

Subcritical insability of viscoelastic flow over a circular cylinder: A numerical study

In this paper, we discuss whether the instability of viscoelastic flow around a circular cylinder is subcritical or supercritical by numerical simulation. The Oldroyd-B model is selected to describe the viscoelastic constitutive relationship. The Log-conformation reformulation is employed to stabilize numerical simulation. The parameter ranges investigated are the Reynolds numbers ($Re$) spanning from 5 to 100 and the Weissenberg number ($Wi$) spanning from 0 to 10, with a fixed viscosity ratio of $\beta = 0.9$. Simulations are performed under two paths, i.e., 1) increasing $Re$ (or $Wi$) and 2) decreasing $Re$ (or $Wi$) slowly and gradually from one state to the next. The results show that the statistical solutions such as the time-averaged velocity obtained along the two paths are not identical over certain parameter range, which is around the transition point from the steady to unsteady flow. This loading path dependence behaviour indicates that the flow instability is subcritical.

physics.flu-dyn↗
arXiv2022

Effect of wall slip on laminar flow past a circular cylinder

A numerical study of two-dimensional flow past a confined circular cylinder with slip wall is performed. A dimensionless number, Knudsen number ($Kn$) is used to describe the slip length of cylinder wall. The Reynolds number ($Re$) and Knudsen number ($Kn$) ranges considered are $Re = [1, 180]$ and $Kn = [0, \infty)$, respectively. Time-averaged flow separation angle ($\bar{\theta_s}$), dimensionless recirculation length ($\bar{L_s}$) and the tangential velocity ($\bar{u_{\tau}}$) distributed on the cylinder's wall, drag coefficient ($\bar{C_d}$) and drag reduction ($DR$) are investigated. The time-averaged tangential velocity distribution on the cylinder's wall fit well with the formula $\bar{u_{\tau}} = [\frac{\alpha}{1+{\beta}e^{-{\gamma}({\pi}-{\theta})}}+{\delta}]sin(\theta) $, where the coefficients ($\alpha$, $\beta$, $\gamma$, $\delta$) are related with $Re$ and $Kn$. Several scaling-laws are found, $log(\bar{u_{{\tau}max}})\sim{log(Re)}$ and $\bar{u_{{\tau}max}}\sim{Kn}$ for low $Kn$, ($\bar{u_{{\tau}max}}$ is the maximum tangential velocity on the cylinder's wall), $log(DR)\sim{log(Re)}$ ($Re\leq45$ and $Kn\leq0.1$), $log(DR)\sim{log(Kn)}$ ($Kn\leq0.05$). At low $Re$, $DR_v$ (the friction drag reduction) is the main source of $DR$. However, $DR_p$ (the differential pressure drag reduction) contributes the most to $DR$ at high $Re$ ($Re>\sim60$) and $Kn$ over a critical number. $DR_v$ is found almost independent to $Re$.

physics.flu-dyn↗
arXiv2022

Wall-induced translation of a rotating particle in viscoelastic fluid

Shear-thinning and viscoelasticity are two non-Newtonian fluid properties widely existing in biological fluids. In this study, we found that the translation motion of a rotating particle near a wall speed up firstly, and then slows down with enhancement of fluid viscoelasticity, which is different from the behavior reported in shear thinning fluid (Chen et al. J. Fluid Mech. 2021, 927). Our research is carried out by numerical simulation of Navier-Stokes equations combined with Oldroyd-B constitutive model. This work is expected to be helpful to understand the movement of a rotating sphere near a wall in complex fluids comprehensively.

physics.flu-dyn↗
arXiv2022

Simulation of flow induced vibration of a cylinder in an expansion tube

In this study, a series of simulations are conducted to investigate the motion of a small cylinder in an expansion tube, focusing on two-dimensional dynamics. These simulations are performed on the FLUENT platform employing the Overset function. The collision between the cylinder and the tube wall is modeled as a positive rigid body collision without losing energy. Two key parameters, the dimensionless gravity (Mg*) and the Reynolds number (Re), were explored within the ranges of 4.9-79.4 and 1-300, respectively. Two types of inflow are considered: the invariable inflow or superimposed a sinusoidal inflow of periodical fluctuation. For invariable inflow, three motion modes (drainage mode, balance mode and vibration mode) are found in the phase diagrams of (Mg*, Re). For an invariable inflow, the high-amplitude vibrations of a cylinder is proved to be widespread in the Reynolds number range from 5 to 40. Additionally, the scenario involving Re =300, Mg* =39.25 with sinusoidal periodic fluctuation incoming flow demonstrated intense vibrations of the cylinder. The behavior of the two-dimensional cylinder can be approximated as a simplified version of a three-dimensional sphere when the spherical motion is disregarded. Our research may help to understand this ancient flow problem.

physics.flu-dyn↗
arXiv2022

Wake asymmetry weakening in viscoelastic fluids: Numerical discovery and mechanism exploration

Viscoelasticity weakens the asymmetry of laminar shedding flow behind a blunt body in a free domain. In the present study, this finding is confirmed by four unsteady viscoelastic flows with asymmetric flow configuration, i.e., flow over an inclined flat plate with various angles of incidence, flow over a rotating circular cylinder, flow over a circular cylinder with asymmetric slip boundary distribution, and flow over an inclined row of eight equally closely spaced circular cylinders (which can be considered as a single large blunt body) through direct numerical simulation combined with the Peterlin approximation of the finitely extensible nonlinear elastic (FENE-P) model. At high Weissenberg number, an arc shape region with high elastic stress, which is similar to shock wave, forms in the frontal area of the blunt body. This region acts as a stationary shield to separate the flow into different regions. Thus, the free stream resembles to pass this shield instead of the original blunt body. As this shield has symmetric feature, the wake flow restores symmetry.

physics.flu-dyn↗
arXiv2022

Numerical Study of Viscoelastic Upstream Instability

In this work, we report numerical results on the flow instability and bifurcation of a viscoelastic fluid in the upstream region of a confined cylinder in a narrow channel. Two-dimensional direct numerical simulations based on the FENE-P model (the finite-extensible nonlinear elastic model with the Peterlin closure) are conducted with numerical stabilization techniques. Our results show that the macroscopic viscoelastic constitutive relation can capture the viscoelastic upstream instability reported in previous experiments for low-Reynolds-number flows. The numerical simulations reveal that the non-dimensional recirculation length ($L_D$) is affected by the cylinder blocking rate ($BR$), the Weissenberg number ($Wi$), the viscosity ratio ($\beta$), and the maximum polymer extension ($L$). Close to the onset of upstream recirculation, depending on the values of $L$ and $\beta$, the bifurcation can be supercritical or subcritical. $\beta$ has a nonlinear influence on the upstream recirculation length. This work contributes to our theoretical understanding of this new instability mechanism in viscoelastic wake flows.

physics.flu-dyn↗