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[CT109]

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : The central region of galaxies can be infinitesimally thin gaseous disks due to the angular moment conservation. Dynamic of gaseous disks is significant for probing the gas flows inward/outward to the origin of galaxies. Moreover, self-gravitational force calculation should be concerned during the evolution of galaxies. We can use the sparse fast Fourier transform (sFFT) to preserve the nearly linear complexity $O(N\log N)$ for numerical calculation based on adaptive mesh refinement (AMR) in this presentation.
Classification : 65M80, 42A16, 42A38
Author(s) :
- Chien-Chang Yen (Fu Jen Catholic University)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : The oxidation behaviour of Ti-6Al-4V at high temperatures was modelled using a partial differential equation. In this approach, the formation of oxide scale is simulated by following an isothermal oxidation process at various controlled temperatures and time intervals at the surface of the alloy, allowing the prediction of mass gain, oxygen diffusion coefficient, and oxide scale thickness. Further experimental work is compared to validate the results.
Classification : 65M99
Author(s) :
- HAFIZAH FARHAH SAIPOL (Department of Management Technology, MALAYSIA JAPAN INTERNATIONAL INSTITUTE OF TECHNOLOGY, UNIVERSITI TEKNOLOGI MALAYSIA)
- Aezal Muhammad Faim (Razak Faculty of Technology & Informatics, UTM KL)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : We develop a Diffuse interface numerical method that simulates the miscible Viscous-Fingering instability in highly convection-dominated regimes (Péclet number > 10000). The developed finite volume scheme uses a two-point flux approximation (TPFA) for Darcy law and a fifth-order Weighted Essentially Non-Oscillatory(WENO) approximation for the convection term of the transport equation. The details of the numerical scheme and simulation results that agree excellently with existing numerical or experimental data will be discussed in this talk.
Classification : 65Mxx, 35Qxx, 76Dxx, 76Sxx, 76Rxx
Author(s) :
- Surya Narayan Maharana (Indian Institute of Technology Ropar)
- Manoranjan Mishra (Indian Institute of Technology Ropar, India)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : Neural network methods have been lately used to solve partial differential equations (PDEs) and dynamical systems. These approaches have been developed into a novel research field of applied mathematics. In this talk, we develop a novel numerical algorithm that incorporates machine learning and artificial intelligence to solve PDEs. Using the Wavelet-Galerkin framework, we propose the neural network method to learn multiple instances of the solutions for different types of PDEs. The proposed neural network is applied to general 1D and 2D PDEs with various boundary conditions as well as convection-dominated PDEs that exhibit strong boundary layer behavior.
Classification : 65Mxx, 65Nxx
Author(s) :
- VIJAY KUMAR PATEL (Vellore Institute of Technology Bhopal)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : In this talk, the $H^2$ stability of two types of the first order Euler implicit/explicit-SAV schemes for the Navier-Stokes equations with finite element discretization is studied with smooth or non-smooth initial data. In the literature, the first order Euler implicit/explicit scheme for the Navier-Stokes for the initial data $u_0$ in $H^{\alpha}$ with $\alpha =1,2$ and the Euler semi-implicit/explicit scheme for the initial data $u_0$ in $H^0$ have been proven to have $H^2-$ almost unconditional stability. In this talk, with the help of scalar auxiliary variable approach, the $H^2$ unconditional stability of two types of the first order Euler implicit/explicit-SAV schemes for the Navier-Stokes equations for the initial data $u_0$ in $H^{\alpha}$ with $\alpha =0, 1,2$ are established, which improve the classical one. Numerical experiments are presented to support the stability results. This is joint work with Teng-Yuan Chang.
Classification : 65Mxx, 86-08, 76Bxx
Author(s) :
- Ming-Cheng Shiue (National Yang Ming Chiao Tung University)
- TENG-YUAN Chang (National Yang Ming Chiao Tung University)