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A New Second Order numerical scheme for Solving Forward Backward Stochastic Differential Equations with Jumps

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Applied Mathematics 2016年第12期7卷 1408-1414页

作者： Hongqiang Zhou Yang Li Zhe Wang College of Science University of Shanghai for Science and Technology Shanghai China

In this paper, we propose a new second order numerical scheme for solving backward stochastic differential equations with jumps with the generator linearly depending on . And we theoretically prove that the convergen... 详细信息

关键词： numerical scheme Error Estimates Backward Stochastic Differential Equations

Lagrangian model of zooplankton dispersion:numerical schemes comparisons and parameter sensitivity tests

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Chinese Journal of Oceanology and Limnology 2011年第2期29卷 438-445页

作者：丘仲锋 Andrea M.DOGLIOLI 何宜军 Francois CARLOTTI Key Laboratory of Ocean Circulation and Waves Institute of Oceanology CAS Laboratoire d'Ocanographie Physique et Biogochimie Aix Marseille UniversiteCNRSUMR 6535MarseilleFrance

This paper presents two comparisons or tests for a Lagrangian model of zooplankton dispersion:numerical schemes and time ***,we compared three numerical schemes using idealized *** show that the precisions of the advanced Adams-Bashfold-Moulton(ABM) method and the Runge-Kutta(RK) method were in the same order and both were much higher than that of the Euler ***,the advanced ABM method is more efficient than the RK method in computational memory requirements and time *** therefore chose the advanced ABM method as the Lagrangian particle-tracking ***,we performed a sensitivity test for time steps,using outputs of the hydrodynamic model,*** show that the time step choices depend on the fluid response time that is related to the spatial resolution of velocity *** method introduced by Oliveira et *** 2002 is suitable for choosing time steps of Lagrangian particle-tracking models,at least when only considering advection.

关键词： Lagrangian numerical scheme time steps zooplankton

SUPPLEMENT AND IMPROVEMENT OF HOLLY-PREISSMANN scheme

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Journal of Hydrodynamics 2004年第4期16卷 468-473页

作者： XIEZuo-tao ZHANGXiao-feng TANGuang-ming StateKeyLaboratoryofWaterResourcesandHydropowerEngineeringScience WuhanUniversity430072China

Using the undetermined coefficient method, Holly-Preissmann scheme isimproved effectively. The scheme with the minus velocity is added, and a new conservative scheme isalso presented on the basis of original scheme. T... 详细信息

关键词： holly-preissmann scheme conservative convection equation numerical scheme undetermined coefficient method

Simulation of a Shock Tube with a Small Exit Nozzle

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Journal of Thermal Science 2018年第1期27卷 34-38页

作者： Yigang Luan Matthias Olzmann Franco Magagnato Harbin Engineering University HarbinChina Karlsruhe Institute of Technology(KIT) Institute of Physical ChemistryKaiserstrasse 1276131 KarlsruheGermany Karlsruhe Institute of Technology(KIT) Institute of Fluid MechanicsKaiserstrasse 1276131 KarlsruheGermany

Shock tubes are frequently used to rapidly heat up reaction mixtures to study chemical reaction mechanisms and kinetics in the field of combustion chemistry [1]. In the present work, the flow field inside a shock tube with a small nozzle in the end plate has been investigated to support the analysis of reacting chemical mixtures with an attached mass spectrometer and to clarify whether the usual assumptions for the flow field and the related ther- modynamics are fulfilled. In the present work, the details of the flow physics inside the tube and the flow out of the nozzle in the end plate have been investigated. Due to the large differences in the typical length scales and the large pressure ratios of this special device, a very strong numerical stiffness prevails during the simulation process. Second-order ROE numerical schemes have been employed to simulate the flow field inside the shock tube. The simulations were performed with the commercial code ANSYS Fluent [2]. Axial-symmetric boundary conditions are employed to reduce the consumption of CPU time. A density-based transient scheme has been used and vali- dated in terms of accuracy and efficiency. The simulation results for pressure and density are compared with ana- lytical solutions. numerical results show that a density-based numerical scheme performs better when dealing with shock-tube problems [5]. The flow field near the nozzle is studied in detail, and the effects of the nozzle to pressure and temperature variations inside the tube are invcstigatcd. The results show that this special shock-tube setup can be used to study high-temperature gas-phase chemical reactions with reasonable accuracy.

关键词： CFD shock tube low pressure numerical scheme

A scheme for improving computational efficiency of quasi-two-dimensional model

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Journal of Hydrodynamics 2017年第2期29卷 243-250页

作者： Tae Uk Jang 伍悦滨徐莹孙强 Department of Mechanics KimⅡSung UniversityPyong YangD.P.R.Korea School of Municipal and Environmental Engineering Harbin Institute of TechnologyHarbin 150090China State Key Laboratory of Urban Water Resource and Environment Harbin Institute of TechnologyHarbin 150090China School of Energy and Architecture Harbin University of CommerceHarbin 150028China

The quasi-2D model, taking into account the axial velocity profile in the cross section and neglecting the convective term in the 2-D equation, can more accurately simulate the water hammer than the 1-D model using the cross-sectional mean velocity. However, as compared with the 1-D model, the quasi-2D model bears a higher computational burden. In order to improve the computational efficiency, the 1-D method is proposed to be used to solve directly the pressure head and the discharge in the quasi-2D model in this paper, based on the fact that the pressure head obtained as the solution of the two-dimensional characteristic equation is identical to that solved by the 1-D characteristic equations. The proposed scheme solves directly the 1-D characteristic equations for the pressure head and the discharge using the MOC and solves the 2-D characteristic equation for the axial velocities in order to calculate the wall shear stress. If the radial velocity is needed, it can be evaluated easily by an explicit equation derived from the explicit 2-D characteristic equation. In the numerical test, the accuracy and the efficiency of the proposed scheme are compared with two existing quasi-two-dimensional models using the MOC. It is shown that the proposed scheme has the same accuracy as the two quasi-2D models, but requires less computational time. Therefore, it is efficient to use the proposed scheme to simulate the 2-D water hammer flows.

关键词： Water hammer method of characteristics numerical scheme pipe quasi-2D model

Comparative Thermal Performance in SiO_(2)–H_(2)O and (MoS_(2)–SiO_(2))–H_(2)O Over a Curved Stretching Semi-Infinite Region: A numerical Investigation

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Computers, Materials & Continua 2021年第1期66卷 947-960页

作者： Basharat Ullah Umar Khan Hafiz Abdul Wahab Ilyas Khan Dumitru Baleanu Kottakkaran Sooppy Nisar Department of Mathematics and Statistics Hazara UniversityMansehra21120Pakistan Faculty of Mathematics and Statistics Ton Duc Thang UniversityHo Chi Minh City72915Vietnam Department of Mathematics Cankaya UniversityAnkaraTurkey Institute of Space Sciences Magurele077125Romania Department of Medical Research China Medical University HospitalChina Medical UniversityTaichungTaiwan Department of Mathematics College of Arts and SciencesWadi Aldawaser11991Prince Sattam Bin Abdulaziz UniversityAl KharjSaudi Arabia

The investigation of Thermal performance in nanofluids and hybrid nanofluids over a curved stretching infinite region strengthens its roots in engineering and ***,the comparative thermal analysis in SiO_(2)–H_(2)O and(MoS_(2)–SiO_(2))–H_(2)O is conducted over curved stretching *** model is reduced in the dimensional version via similarity transformation and then treated *** velocity and thermal behavior for both the fluids is decorated against the preeminent *** the analysis,it is examined that the motion of under consideration fluids declines against Fr and.The thermal performance enhances for higher volumetric fraction and.Further,it is noticed that thermal performance prevailed in(MoS_(2)–SiO_(2))–H_(2)O throughout the ***,(MoS_(2)–SiO_(2))–H_(2)O is better for industrial and engineering uses where high heat transfer is required to accomplished different processes of production.

关键词： Thermal performance curved surface SiO_(2)–H_(2)O and(MoS_(2)–SiO_(2))–H_(2)O shear stresses Nusselt number numerical scheme

Al_(2)O_(3) andγAl_(2)O_(3) Nanomaterials Based Nanofluid Models with Surface Diffusion:Applications for Thermal Performance in Multiple Engineering Systems and Industries

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Computers, Materials & Continua 2021年第2期66卷 1563-1576页

作者： Adnan Umar Khan Naveed Ahmed Syed Tauseef Mohyud-Din Ilyas Khan Dumitru Baleanu Kottakkaran Sooppy Nisar Department of Mathematics Mohi-ud-Din Islamic UniversityNerian Sharif12080Pakistan Department of Mathematics and Statistics Hazara UniversityMansehra21120Pakistan Department of Mathematics Faculty of SciencesHITEC UniversityTaxila Cantt47070Pakistan University of Multan Multan66000Pakistan Faculty of Mathematics and Statistics Ton Duc Thang UniversityHo Chi Minh City72915Vietnam Department of Mathematics Cankaya UniversityAnkaraTurkey Institute of Space Sciences Magurele077125Romania Department of Medical Research China Medical University HospitalChina Medical UniversityTaichungTaiwan Department of Mathematics College of Arts and SciencesPrince Sattam bin Abdulaziz UniversityWadi Aldawaser11991Saudi Arabia

Thermal transport investigation in colloidal suspensions is taking a significant research *** applications of these fluids are found in various industries,engineering,aerodynamics,mechanical engineering and medical sciences etc.A huge amount of thermal transport is essential in the operation of various industrial production *** is a fact that conventional liquids have lower thermal transport characteristics as compared to colloidal *** colloidal suspensions have high thermal performance due to the thermophysical attributes of the nanoparticles and the host ***,researchers focused on the analysis of the heat transport in nanofluids under diverse *** such,the colloidal analysis of H_(2)O composed byγAl_(2)O_(3)and Al_(2)O_(3)is conducted over an elastic *** governing flow models ofγAl_(2)O_(3)/H_(2)O and Al_(2)O_(3)/H_(2)O is reduced in the dimensionless form by adopting the described similarity *** colloidal models are handled by implementing the suitable numerical technique and provided the results for the velocity,temperature and local thermal performance rate against the multiple flow *** the presented results,it is shown that the velocity of Al_(2)O_(3)–H_(2)O increases promptly against a high Reynolds number and it decreases for high-volume *** significant contribution of the volumetric fraction is examined for thermal enhancement of *** temperature of Al_(2)O_(3)–H_(2)O andγAl_(2)O_(3)–H_(2)O significantly increases against a higherϕ.Most importantly,the analysis shows thatγAl_(2)O_(3)–H_(2)O has a high local thermal performance rate compared to Al_(2)O_(3)–H_(2)***,it is concluded thatγAl_(2)O_(3)–H_(2)O is a better heat transfer fluid and is suitable for industrial and technological uses.

关键词： Thermal performance Al_(2)O_(3)andγAl_(2)O_(3)nanomaterials thermophysical attributes of nanomaterials stretching cylinder suction/blowing numerical scheme nusselt number

Transmission dynamics of Hand-Foot-Mouth Disease with partial immunity through non-integer derivative

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生物数学学报:英文版 2023年第6期16卷 149-173页

作者： Rashid Jan Salah Boulaaras Sultan Alyobit Muhammad Jawad Department of Mathematics University of Swabi Swabi 23561Khyber PakhtunkhwaPakistan Department of Mathematics College of Sciences and Arts Qassim UniversityAr RassSaudi Arabia Department of Mathematics College of Science 8 Arts King Abdulaziz UniversityRabighSaudi Arabia

In this paper,we formulate the transmission phenomena of Hand-Foot-Mouth Disease(HFMD)through non-integer *** interrogate the biological meaningful results of the recommended system of *** basic reproduction number is determined through next generation method and the impact of different parameters on the reproduction number is examined with the help of partial rank correlation coeficient(PRCC)*** addition,we concentrated on qualitative analysis and dynamical behavior of HFMD ***'s and Schaefer's fixed-point theorems are used to analyze the uniqueness and existence of the solution of the proposed HFMD *** HFMD system's Ulam-Hyers stability has been confirmed to be *** highlight the impact of the parameters on the dynamics of HFMD,we performed several simulations through numerical scheme to conceptualize the transmission route of the *** be more specific,numerical simulations are used to visualize the effect of input parameters on the systems *** have shown the key input parameters of the system for the control of infection in the society.

关键词： Hand-Foot-Mouth Disease fractional derivatives mathematical model threshold parameter numerical scheme dynamical behavior

A Generalized Stationary Algorithm for Resonant Tunneling:Multi-Mode Approximation and High Dimension

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Communications in Computational Physics 2011年第9期10卷 882-898页

作者： Naoufel Ben Abdallah Hao Wu Department of Mathematical Sciences Tsinghua UniversityBeijing10084China Institut de Math´ematiques de Toulouse Universite Paul Sabatier118route de Narbonne31062 Toulouse CedexFrance.

The multi-mode approximation is presented to compute the interior wave function of Schr¨odinger *** idea is necessary to handle the multi-barrier and high dimensional resonant tunneling problems where multiple eigenv... 详细信息

关键词： Schrodinger equation numerical scheme resonant tunneling multi-mode approximation high dimension.