arXiv subjects

Chaoyi Cai

Publications and source records attributed to Chaoyi Cai.

7 recordsLinked to original sources

arXiv2026

Beyond Free-Stream Preservation: Transport Polynomial Exactness for Moving-Mesh Methods under Arbitrary Mesh Motion

High-order moving-mesh methods can effectively reduce numerical diffusion, but their formal accuracy typically relies on the regularity of the mesh velocity. This dependency creates a fundamental conflict in the numerical solution of hyperbolic conservation laws, where solution-driven adaptation may induce nonsmooth mesh motion, thereby degrading convergence order. We introduce \emph{transport polynomial exactness} (TPE($k$)), a mesh-motion-independent criterion that generalizes classical free-stream preservation (TPE(0)) to the exact advection of degree-$k$ polynomials. We show that the classical geometric conservation law (GCL) is insufficient to ensure TPE($k$) for $k \ge 1$ due to mismatches in higher-order geometric moments. To resolve this, we propose \emph{evolved geometric moments} (EGMs), obtained by solving auxiliary transport equations discretized compatibly with the physical variables. We rigorously prove that second-degree EGMs evolved via the third-order strong stability preserving Runge--Kutta (SSPRK3) method coincide with the exact geometric moments. This exactness arises from a \emph{superconvergence} mechanism wherein SSPRK3 reduces to Simpson's rule for EGM evolution. Leveraging this result, we construct a third-order conservative finite-volume rezoning moving-mesh scheme. The scheme satisfies the TPE(2) property for \emph{arbitrary mesh motion} and \emph{any pseudo-time step size}, thereby naturally accommodating spatiotemporally discontinuous mesh velocity. Crucially, this \emph{breaks the efficiency bottleneck} in the conventional advection-based remapping step and reduces the required pseudo-time levels from $\mathcal{O}(h^{-1})$ to $\mathcal{O}(1)$ under bounded but discontinuous mesh velocity. Numerical experiments verify exact quadratic transport and stable third-order convergence under extreme mesh deformation, demonstrating substantial efficiency gains.

math.NA↗

arXiv2025

Geometric-Perturbation-Robust Cut-Cell Scheme for Two-Material Flows: Exact Pressure-Equilibrium Preservation and Rigorous Analysis

Preserving pressure equilibrium across material interfaces is critical for the stability of compressible multi-material flow simulations, yet most interface-fitted sharp-interface schemes are notoriously sensitive to interface geometry: even slight perturbations of the captured (or tracked) interface can trigger large spurious pressure oscillations. We present a cut-cell method that is geometric-perturbation-robust (GPR) for the compressible two-material flows. By construction, the scheme provably preserves exact interfacial pressure equilibrium in the presence of small interface-position errors. The key is a strict consistency between the conserved variables and the geometric moments (i.e., the integrals of monomials) of every cut cell. We formulate auxiliary transport equations, whose discrete solutions furnish evolved geometric moment, these geometric moments remain perfectly synchronized with the conserved variables -- even on a deforming mesh. Surpassing the classical geometric conservation law, our approach keeps all higher-order geometric moments consistent, thereby eliminating accuracy loss due to geometric mismatches. To prevent the reconstruction step from destroying pressure equilibrium, we introduce the notion of equilibrium-compatible (EC) reconstructions. A carefully designed modification equips any conventional weighted essentially non-oscillatory (WENO) reconstruction with the EC property; we detail a third-order EC multi-resolution WENO (EC-MRWENO) variant. The tight coupling of EC-MRWENO with the evolved moments yields the first cut-cell solver that is simultaneously provably GPR and genuinely high-order: it attains second-order accuracy precisely at material interfaces, while preserving third-order accuracy in smooth regions. Extensive two-dimensional tests confirm the framework's robustness, accuracy and stability under geometric perturbations and topology changes.

math.NA↗

arXiv2024

Provably Convergent and Robust Newton-Raphson Method: A New Dawn in Primitive Variable Recovery for Relativistic MHD

A long-standing and formidable challenge faced by all conservative schemes for relativistic magnetohydrodynamics (RMHD) is the recovery of primitive variables from conservative ones. This process involves solving highly nonlinear equations subject to physical constraints. An ideal solver should be "robust, accurate, and fast -- it is at the heart of all conservative RMHD schemes," as emphasized in [S.C. Noble et al., ApJ, 641:626-637, 2006]. Despite over three decades of research, seeking efficient solvers that can provably guarantee stability and convergence remains an open problem. This paper presents the first theoretical analysis for designing a robust, physical-constraint-preserving (PCP), and provably (quadratically) convergent Newton-Raphson (NR) method for primitive variable recovery in RMHD. Our key innovation is a unified approach for the initial guess, devised based on sophisticated analysis. It ensures that the NR iteration consistently converges and adheres to physical constraints. Given the extreme nonlinearity and complexity of the iterative function, the theoretical analysis is highly nontrivial and technical. We discover a pivotal inequality for delineating the convexity and concavity of the iterative function and establish theories to guarantee the PCP property and convergence. We also develop theories to determine a computable initial guess within a theoretical "safe" interval. Intriguingly, we find that the unique positive root of a cubic polynomial always falls within this interval. Our PCP NR method is versatile and can be seamlessly integrated into any RMHD scheme that requires the recovery of primitive variables, potentially leading to a broad impact in this field. As an application, we incorporate it into a discontinuous Galerkin method, resulting in fully PCP schemes. Several numerical experiments demonstrate the efficiency and robustness of the PCP NR method.

math.NA↗

arXiv2023

Provably convergent Newton-Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodynamics

The relativistic hydrodynamics (RHD) equations have three crucial intrinsic physical constraints on the primitive variables: positivity of pressure and density, and subluminal fluid velocity. However, numerical simulations can violate these constraints, leading to nonphysical results or even simulation failure. Designing genuinely physical-constraint-preserving (PCP) schemes is very difficult, as the primitive variables cannot be explicitly reformulated using conservative variables due to relativistic effects. In this paper, we propose three efficient Newton--Raphson (NR) methods for robustly recovering primitive variables from conservative variables. Importantly, we rigorously prove that these NR methods are always convergent and PCP, meaning they preserve the physical constraints throughout the NR iterations. The discovery of these robust NR methods and their PCP convergence analyses are highly nontrivial and technical. As an application, we apply the proposed NR methods to design PCP finite volume Hermite weighted essentially non-oscillatory (HWENO) schemes for solving the RHD equations. Our PCP HWENO schemes incorporate high-order HWENO reconstruction, a PCP limiter, and strong-stability-preserving time discretization. We rigorously prove the PCP property of the fully discrete schemes using convex decomposition techniques. Moreover, we suggest the characteristic decomposition with rescaled eigenvectors and scale-invariant nonlinear weights to enhance the performance of the HWENO schemes in simulating large-scale RHD problems. Several demanding numerical tests are conducted to demonstrate the robustness, accuracy, and high resolution of the proposed PCP HWENO schemes and to validate the efficiency of our NR methods.

math.NA↗

arXiv2018

Electronic transport properties of Co cluster-decorated graphene

Interactions of magnetic elements with graphene may lead to various electronic states that have potential applications. We report an in-situ experiment in which the quantum transport properties of graphene are measured with increasing cobalt coverage in continuous ultra-high vacuum environment. The results show that e-beam deposited cobalt forms clusters on the surface of graphene, even at low sample temperatures. Scattering of charge carriers by the absorbed cobalt clusters results in the disappearance of the Shubnikov-de Haas (SdH) oscillations and the appearance of negative magnetoresistance (MR) which shows no sign of saturation up to an applied magnetic field of 9 T. We propose that these observations could originate from quantum interference driven by cobalt disorder and can be explained by the weak localization theory.

cond-mat.mes-hall↗

arXiv2017

Gate Tunable Magneto-resistance of Ultra-Thin WTe2 Devices

In this work, the magneto-resistance (MR) of ultra-thin WTe2/BN heterostructures far away from electron-hole equilibrium is measured. The change of MR of such devices is found to be determined largely by a single tunable parameter, i.e. the amount of imbalance between electrons and holes. We also found that the magnetoresistive behavior of ultra-thin WTe2 devices is well-captured by a two-fluid model. According to the model, the change of MR could be as large as 400,000%, the largest potential change of MR among all materials known, if the ultra-thin samples are tuned to neutrality when preserving the mobility of 167,000 cm2V-1s-1 observed in bulk samples. Our findings show the prospects of ultra-thin WTe2 as a variable magnetoresistance material in future applications such as magnetic field sensors, information storage and extraction devices, and galvanic isolators. The results also provide important insight into the electronic structure and the origin of the large MR in ultra-thin WTe2 samples.

cond-mat.mtrl-sci↗

arXiv2016

On the quantum spin Hall gap of monolayer 1T'-WTe2

Quantum spin Hall (QSH) materials are two-dimensional systems exhibiting insulating bulk and helical edge states simultaneously. A QSH insulator processes topologically non-trivial edge states protected by time-reversal symmetry, so that electrons can propagate unscattered. Realization of such topological phases enables promising applications in spintronics, dissipationless transport and quantum computations. Presently, realization of such QSH-based devices are limited to complicated heterostructures. Monolayer 1T'-WTe2 was predicted to be semimetallic QSH materials, though with a negative band gap. The quasi-particle spectrum obtained using hybrid functional approach shows directly that the quantum spin Hall gap is positive for monolayer 1T'-WTe2. Optical measurement shows a systematic increase in the interband relaxation time with decreasing number of layers, whereas transport measurement reveals Schottcky barrier in ultrathin samples, which is absent for thicker samples. These three independent pieces of evidence indicate that monolayer 1T'-WTe2 is likely a truly 2-dimensional quantum spin Hall insulator.

cond-mat.mtrl-sci↗