Adaptive ADI difference solution of quenching problems based on the 3D convection–reaction–diffusion equation
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Xiaoliang Zhu
Abstract
The 3D quenching problem reflecting solid-burn scene based on convection–reaction–diffusion equation is creatively concerned in this work. The spatial derivatives of original equation are discretized by Taylor series and the temporal derivatives are approximated by the Crank–Nicolson (CN) method. After the discrete schemes are arranged, an alternating direction implicit (ADI) scheme on adaptive grid is constructed to interpret quenching phenomena of the three-dimension (3D) equation with singularity source. Quenching time, quenching domain, and characteristics relative to temperature as well as variation of temperature over time are achieved via scientific experiment and analysis. Comparing with the 1D or 2D problem, it is harder for the 3D problem to produce quenching phenomena. Regardless of different convection functions, it can form quenching behaviors through experiments when only the elements which include degeneracy parameter, convection parameters, and domain sizes are configured properly. We hope all this can offer references for the 3D engineering problem. At the same time, it will offer support to research the relationship between quenching phenomena and degeneracy parameter, convection parameters, and domain sizes in the future, respectively.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: This work is partially supported by National Natural Science Foundation of China (11772165, 11961054, 11902170), National Natural Science Foundation of Ningxia (2020AAC03059), and National Youth Top-notch Talent Support Program of Ningxia.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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- Optimal control of non-instantaneous impulsive second-order stochastic McKean–Vlasov evolution system with Clarke subdifferential
- Generalized forms of fractional Euler and Runge–Kutta methods using non-uniform grid
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Frequency responses for induced neural transmembrane potential by electromagnetic waves (1 kHz to 1 GHz)
- Investigating existence results for fractional evolution inclusions with order r ∈ (1, 2) in Banach space
- Optimal control of non-instantaneous impulsive second-order stochastic McKean–Vlasov evolution system with Clarke subdifferential
- Generalized forms of fractional Euler and Runge–Kutta methods using non-uniform grid
- Controllability of coupled fractional integrodifferential equations
- A new generalized approach to study the existence of solutions of nonlinear fractional boundary value problems
- Rational soliton solutions in the nonlocal coupled complex modified Korteweg–de Vries equations
- Buoyancy driven flow characteristics inside a cavity equiped with diamond elliptic array
- Analysis and numerical effects of time-delayed rabies epidemic model with diffusion
- Two occurrences of fractional actions in nonlinear dynamics
- Multiwave interaction solutions for a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics
- Effects of mixed time delays and D operators on fixed-time synchronization of discontinuous neutral-type neural networks
- Solvability and stability of nonlinear hybrid ∆-difference equations of fractional-order
- Weak and strong boundedness for p-adic fractional Hausdorff operator and its commutator
- Simulation and modeling of different cell shapes for closed-cell LM-13 alloy foam for compressive behavior
- Pandemic management by a spatio–temporal mathematical model
- Adaptive ADI difference solution of quenching problems based on the 3D convection–reaction–diffusion equation
- Null controllability of Hilfer fractional stochastic integrodifferential equations with noninstantaneous impulsive and Poisson jump
- Application of modified Mickens iteration procedure to a pendulum and the motion of a mass attached to a stretched elastic wire
- Modeling the spatiotemporal intracellular calcium dynamics in nerve cell with strong memory effects
- Switched coupled system of nonlinear impulsive Langevin equations involving Hilfer fractional-order derivatives
- Improving the dynamic behavior of the plate under supersonic air flow by using nonlinear energy sink
