Article
Computer Science, Interdisciplinary Applications
Matthias Wiesenberger, Raul Gerru, Markus Held
Summary: This paper investigates strategies to numerically integrate closed lines and surfaces defined by iso-contours of toroidally symmetric functions. The grid-transform method shows high order convergence in line, surface, and volume integration, with significantly smaller errors compared to delta-function methods. However, a delta-function method based on Gaussian representation exhibits qualitative errors in surface integrals near O- and X-points. The paper also introduces a toroidal integration approach that uses toroidal summation and a smoothing kernel to eliminate unphysical oscillations in the simple toroidal average.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Engineering, Mechanical
Chun Li, Yunyun Yang, Hui Liang, Boying Wu
Summary: In this work, two potential high-order geometric flows are proposed by integrating deep neural networks and level set method. The proposed models are demonstrated to be more robust and efficient compared to the state-of-the-art approach through numerical experiments on different input data.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Applied
Fan Zhang, Tiegang Liu, Moubin Liu
Summary: This study proposes a high-order discontinuous Galerkin method to directly solve the advection equation for the LS function in non-conservative form. By applying a linear scaling limiter and a strong stability preserving time discretization scheme, it ensures the strict maximum principle under a suitable CFL condition.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Shumaila Yasmeen, Siraj-Ul-Islam, Rohul Amin
Summary: Higher order Haar wavelet method (HOHWM) is used for second kind integral equations, including Fredholm and Volterra types. The method also works for nonlinear problems. HOHWM shows second and fourth-order convergence, which is an improvement compared to the first-order convergence of Haar wavelet method (HWM).
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Peter Frolkovic, Nikola Gajdosova
Summary: This paper presents compact semi-implicit finite difference schemes for solving advection problems using level set methods. Through numerical tests and stability analysis, the accuracy and stability of the proposed schemes are verified.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mechanics
Qi Xia, Hongming Zong, Tielin Shi, Hui Liu
Summary: This paper presents two important extensions of the multiple variable cutting (M-VCUT) level set method for topology optimization of cellular structures: a mapping technique for transferring microstructure prototypes from square cells to quadrilateral cells, and the use of high order cutting functions to enhance geometric representation flexibility. These extensions inherit the advantages of VCUT and M-VCUT methods while enabling more flexible optimization for cellular structures with complex geometry.
COMPOSITE STRUCTURES
(2021)
Article
Computer Science, Interdisciplinary Applications
Dmitri Kuzmin, Jan-Phillip Baecker
Summary: We propose a new method for handling flux boundary conditions imposed on level sets. This method is a diffuse interface version of the shifted boundary method for discretizing conservation laws in embedded domains. We use weak interface conditions and approximate surface integrals with volume integrals. The discretized weak form of the governing equation resembles an immersed boundary finite element method, integrating over a fixed fictitious domain.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Multidisciplinary Sciences
Vahid Reza Hosseini, Farzaneh Yousefi, W. -N. Zou
Summary: This study introduces a novel meshless technique for solving diffusion problems within cell biology, computer graphics, image processing, and fluid flow. It presents a variable-order time fractional diffusion equation and uses a meshfree method based on singular boundary method and dual reciprocity method on three-dimensional arbitrary geometry for numerical solutions. Results confirm the stability and convergent of the proposed method on high-dimensional domains, demonstrating its reliability and accuracy on complex geometries.
JOURNAL OF ADVANCED RESEARCH
(2021)
Article
Mathematics, Applied
Esra Kaya
Summary: In this study, we introduce the sharp function related to the Laplace-Bessel differential operator and investigate its properties on the variable Lebesgue spaces. Moreover, we prove that Riesz-Bessel transforms of high order are bounded on variable Lebesgue spaces L-p(center dot),L-gamma (R-k,+(n)).
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Energy & Fuels
Hiroki Muramatsu, Abhishek L. Pillai, Kenya Kitada, Ryoichi Kurose
Summary: In this study, the evaporation of binary-component fuel droplets was simulated using the Eulerian framework with an extended evaporation model. The results showed a good agreement with experimental data, confirming the capability of the numerical framework to capture the evaporation phenomenon. Parametric simulations were also performed to investigate the influences of different initial compositions and ambient temperatures on the evaporation characteristics of the droplets.
Article
Green & Sustainable Science & Technology
Kan Kan, Zixuan Yang, Pin Lyu, Yuan Zheng, Lian Shen
Summary: The study utilizes large-eddy simulation to investigate the turbulence characteristics and flow structures of water passing a rotating axial-flow pump under various flow-rate working conditions. The results indicate that tip leakage flow dominates at low flow-rates, while flow separation prevails at high flow-rates under off-designed conditions.
Article
Mathematics, Applied
Emre Kirli, Dursun Irk, Melis Zorsahin Gorgulu
Summary: In this study, the Galerkin finite element method with cubic B-spline function is used to obtain the numerical solution of the linear telegraph equation. A fourth order one-step method is employed to discretize the telegraph equation in time, which improves the efficiency and accuracy of the method. Three examples demonstrate the higher accuracy of the proposed method.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Thermodynamics
Harshal S. Raut, Amitabh Bhattacharya, Atul Sharma
Summary: The study uses Direct Numerical Simulations to investigate the impact of base plate oscillations on nucleate boiling heat transfer. The results show the existence of a lock-on regime where the frequency of bubble departure synchronizes with the frequency of plate oscillation. Increasing oscillation amplitude enhances this lock-on effect and also increases the average Nusselt number by around 22%.
INTERNATIONAL JOURNAL OF THERMAL SCIENCES
(2021)
Article
Mathematics, Applied
Ghodsieh Ghanbari, Mohsen Razzaghi
Summary: A new alternative numerical method using fractional-order Chebyshev wavelets to solve variable-order fractional optimal control problems is introduced, providing an exact value for the fractional integration of the given wavelets using regularized beta functions. By applying this formula and the given wavelets, the VO-FOCP is reduced to a system of algebraic equations which can be solved with known methods, with convergence analysis for function approximation. Several numerical examples demonstrate the method's superior accuracy compared to existing methods in the literature.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Computer Science, Theory & Methods
Tong Kang, Dongsheng Wu, Jun Li
Summary: This paper proposes the set-valued pan-integral based on number-valued fuzzy measure and explores its properties. The monotonicity of the set-valued pan-integral is demonstrated using a preorder on the class of all nonempty sets. The linearity of the set-valued pan-integral is shown through an equivalence relation based on the preorder. The relationship between the set-valued pan-integral and the set-valued Choquet integral is discussed, and Chebyshev's inequality of set-valued pan-integrals is proven. An open problem regarding the linearity of the set-valued pan-integral is raised.
FUZZY SETS AND SYSTEMS
(2023)