OOIR: Observatory of International Research

Papers

(The TQCC of Advances in Applied Mathematics and Mechanics is 2. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2022-05-01 to 2026-05-01.)

Article	Citations
Numerical Investigation of the Pulsatile Flow of Viscous Fluid in Constricted Wall Channel with Thermal Radiation	36
A Direct-Forcing Immersed Boundary Projection Method for Thermal Fluid-Solid Interaction Problems	21
On the Characteristic Length Scale for the Synthetic Turbulence Based on the Spalart-Allmaras Model	20
Stokes Flows Imposed Constant Navier Slip Length on Boundary for Domains of Simple Geometry	20
Oversampled Collocation Approximation Method of Functions via Jacobi Frames	17
A New Unified Form of Universal Wall Function	16
A Numerical Study of Integrated Linear Reconstruction for Steady Euler Equations Based on Finite Volume Scheme	16
Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations	15
An Explicit Method for the Coupled Forward Backward Stochastic Differential Equations	11
Ultra-Chaos: An Insurmountable Objective Obstacle of Reproducibility and Replication	9
An Absolutely Stabilized Virtual Element Method for the Incompressible Stokes Equations	9
On the Convergence of a Crank-Nicolson Fitted Finite Volume Method for Pricing European Options Under Regime-Switching Kou’s Jump-Diffusion Models	8
Comparison of Sharp and Diffuse Interface Methods for Radially Symmetric Compressible Multi-Medium Fluid Flows	8
Numerical Computation of Helical Waves in a Finite Circular Cylinder Using Chebyshev Spectral Method	8
A Conservative Upwind Approximation on Block-Centered Difference for Chemical Oil Recovery Displacement Problem	8
Numerical Analysis of Stabilized Second Order Semi-Implicit Finite Element Methods for the Phase-Field Equations	8
A Finite Element Method by Patch Reconstruction for the Quad-Curl Problem Using Mixed Formulations	7
Unconditionally Energy-Dissipation- and Maximum-Bound-Principle-Preserving Scheme for the Time-Fractional Allen-Cahn Equation	7
Thirteen-Velocity Three-Dimensional Multiple-Relaxation-Time Lattice Boltzmann Model for Incompressible Navier-Stokes Equations	7
An Analytical Approach for Nonlinear Buckling Analysis of Torsionally Loaded Sandwich Carbon Nanotube Reinforced Cylindrical Shells with Auxetic Core	7
Weighted Sonine Conditions and Application	7
A First-Order Linear Energy Stable Scheme for the Cahn�Hilliard Equation with Dynamic Boundary Conditions Under the Effect of Hyperbolic Relaxation	7
Prediction of Transition Locations in Regions of the Minor Axis of Hypersonic Elliptic Cones Using the BiGlobal-$e^N$ Method	7
Nonlinear Vibroacoustic Analysis of Functionally Graded Plates in the Thermal Ambiance at Oblique Incidence	6
Numerical Analysis of Two-Grid Block-Centered Finite Difference Method for Two-Phase Flow in Porous Medium	6

Troubled-Cell Indicators Using K-Means Clustering for RKDG Methods on Triangular Meshes and $h$-Adaptive Rectangular Meshes	6
A Spectral Split-Step Pad� Method for Guided Wave Propagation	5
Implicit Runge-Kutta-Nyström Methods with Lagrange Interpolation for Nonlinear Second-Order IVPs with Time-Variable Delay	5
Multi-Resolution WENO Method with Adaptive Linear Weights Using Subcell Strategy	5
Two-Grid Crank-Nicolson Finite Volume Element Method for the Time-Dependent Schrödinger Equation	5
High-Order Unconditionally Energy-Stable Decoupled Method for Phase Field Modeling of Pitting Corrosion with Adaptive Implementation	5
New Finite Volume Mapped Unequal-Sized WENO Scheme for Hyperbolic Conservation Laws	5
DPK: Deep Neural Network Approximation of the First Piola-Kirchhoff Stress	5
A Weak Galerkin Finite Element Method for a $H({\rm curl})$-Elliptic Problem	5
Stability Analysis of Axially Functionally Graded Beams Using the Differential Quadrature Method	5
Two Novel Space-Time Polynomial Particular Solutions Methods for the Time-Dependent Schrödinger Equation	5
A Well-Balanced FVC Scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes	4
A Vertex-Centered Arbitrary Lagrangian-Eulerian Finite Volume Method with Sub-Cells for Two-Dimensional Compressible Flow	4
Nonconforming Finite Element Methods for Two-Dimensional Linearly Elastic Shallow Shell Model	4
Decoupled and Unconditionally Energy Stable Numerical Schemes for the Thermally Coupled Incompressible Magnetohydrodynamics Flow	4
An SAV Method for Imaginary Time Gradient Flow Model in Density Functional Theory	4
Shock Wave Structure of One-Dimensional Hydro-Elastoplastic Riemann Problem with Elastic-Plastic-Fluid Phase Transition	4
Characterizing Natural Convection, Energy, and Thermal Behavior in a Circular Cavity: Finite Element Analysis	4
Explicit, Monotone and Structure-Preserving Finite Difference Methods for Fisher-Kolmogorov-Petrovsky-Piscounov Equation and Allen-Cahn Equation	4
On Field Concentration Between Nearly-Touching Multiscale Inclusions in the Quasi-Static Regime	4
Deep Domain Decomposition Methods: Helmholtz Equation	4
A Fully Discrete Method for Space-Time Fractional Parabolic Problems	4
Convergence Analysis and Error Estimate for Distributed Optimal Control Problems Governed by Stokes Equations with Velocity-Constraint	4
SAV Finite Element Method for the Peng-Robinson Equation of State with Dynamic Boundary Conditions	3
Stability Analysis for Modelling 3D Poroelastic Wave Propagation by High-Order Staggered-Grid Schemes	3
Application of Lattice Boltzmann Method to Simulate Forest Edge	3
Mass-, and Energy-Preserving Sine Pseudo-Spectral Schemes with High-Accuracy for the Coupled Nonlinear Schrödinger Equation	3
A Ciarlet-Raviart Mixed Finite Element Method for Optimal Control Problems Governed by a Fourth Order Bi-Wave Equation	3
Corrected Linear-Galerkin Schemes to Preserve Second-Order Accuracy for Cell-Centered Unstructured Finite Volume Methods	3
The Convergence of Euler-Maruyama Method of Nonlinear Variable-Order Fractional Stochastic Differential Equations	3
Numerical Analysis of Crack-Tip Fields Using a Meshless Method in Linear Elastic Materials	3
An Extension of the Order-Preserving Mapping to the WENO-Z-Type Schemes	3
An Efficient Method for the RCS Reduction of Cavities in the Ground Plane	3
Nonconforming Mixed FEM Analysis for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation with Time-Space Coupled Derivative	3
Petrov-Galerkin Immersed Iso$P_2-P_0$ Interface Method for Solving Stokes Interface Problem	3
Asymptotic Error Analysis for the Discrete Iterated Galerkin Solution of Urysohn Integral Equations with Green’s Kernels	3
Uncertainty Quantification of Store-Separation Simulation Due to Ejector Modeling Using a Monte Carlo Approach with Kriging Model	3
An Adaptive High-Order Surface Finite Element Method for Polymeric Self-Consistent Field Theory on General Curved Surfaces	3
The Random Feature Method for Elliptic Eigenvalue Problems	3
Analysis of Weakly Nonlinear Evolution Characteristics of Flow in the Constant Curvature Bend	3
A Robust Three-Level Time Split High-Order Leapfrog/Crank-Nicolson Scheme for Two-Dimensional Sobolev and Regularized Long Wave Equations Arising in Fluid Mechanics	3
Finite Element Method Coupling Penalty Method for Flexural Shell Model	2
Adaptive Finite Element Method for Simulating Graphene Surface Plasmon Resonance	2
Deep Neural Network for Oscillation Dynamics of Capillary Rise	2
Fully Discrete Schemes with First- and Second-Order Temporal Accuracy for the Incompressible Magnetohydrodynamic Flow Based on the Generalized Scalar Auxiliary Variable Approach	2
A Maximum-Principle-Preserving Finite Volume Scheme for Diffusion Problems on Distorted Meshes	2
Two Efficient Block Preconditioners for the Mass-Conserved Ohta-Kawasaki Equation	2
An Upwind-Block-Centered Multistep Difference Method for a Semiconductor Device and Numerical Analysis	2
An Energy Stable Local Discontinuous Galerkin Method for a Binary Compressible Flow	2
Lattice Boltzmann Model for a Class of Viscous Wave Equation	2

Isotropic Cloak Materials Design Based on the Numerical Optimization Method of the Inverse Medium Problem	2
High Order Deep Domain Decomposition Method for Solving High Frequency Interface Problems	2
The Nonconforming Finite Element Methods for Two Transmission Eigenvalue Problems in Inverse Scattering	2
A High-Order Localized Artificial Diffusivity Scheme for Discontinuity Capturing on 1D Drift-Flux Models for Gas-Liquid Flows	2
Optimizing Thermal Lattice Boltzmann Method on an MT-3000 Processor with Neo-Heterogeneous Strategies	2
Physics-Informed Deep Learning Method for Surrogate Modeling in Elastic Mechanics	2
A Stabilizer-Free Weak Galerkin Finite Element Method for the Stokes Equations	2
Nonpolynomial Jacobi Spectral-Collocation Method for Weakly Singular Fredholm Integral Equations of the Second Kind	2
A Novel Wavelet-Homotopy Galerkin Method for Unsteady Nonlinear Wave Equations	2
A Partial RKDG Method for Solving the 2D Ideal MHD Equations Written in Semi-Lagrangian Formulation on Moving Meshes with Exactly Divergence-Free Magnetic Field	2
Influence of the Radial Inertia Effect on the Propagation Law of Stress Waves in Thin-Walled Tubes	2
Avoiding Small Denominator Problems by Means of the Homotopy Analysis Method	2
A Fast Spatial Two-Grid Raviart-Thomas MFE Algorithm for the Nonlinear Time Fractional Diffusion Equations on Temporal Graded Mesh	2
A New Framework of Convergence Analysis for Solving the General Nonlinear Schrödinger Equation Using the Fourier Pseudo-Spectral Method in Two Dimensions	2
A Second Order Accurate in Time, Energy Stable Finite Element Scheme for the Flory-Huggins-Cahn-Hilliard Equation	2
Two-Relaxation-Time Regularized Lattice Boltzmann Model for Navier-Stokes Equations	2
The Spatial-Temporal Fourth-Order Conservative Characteristic Runge-Kutta Finite Difference Method for Convection-Dominated Diffusion Equation	2
Strong Converge Order of the General One-Step Method for Neutral Stochastic Delay Differential Equations under a Global Monotone Condition	2
High Order Well-Balanced Finite Difference AWENO Scheme for Ripa and Pollutant Transport Systems	2
A Self-Adaptive Algorithm of the Clean Numerical Simulation (CNS) for Chaos	2
Broad Learning System with Preprocessing to Recover the Scattering Obstacles with Far–Field Data	2
A Hessian Recovery Based Linear Finite Element Method for Molecular Beam Epitaxy Growth Model with Slope Selection	2
A Priori Error Estimates for Spectral Galerkin Approximations of Integral State-Constrained Fractional Optimal Control Problems	2
Finite-Time Stability and Instability of Nonlinear Impulsive Systems	2
Spatial-Temporal Adaptive-Order Positivity-Preserving WENO Finite Difference Scheme with Relaxed CFL Condition for Euler Equations with Extreme Conditions	2