Isi Taşinimi İçi̇n Yapisal Olmayan Ağlarda Bi̇r Hizlandirilmiş Süreksi̇z Galerki̇n Metdu: Formülasyonu Ve Doğrulanmasi

Abstract

We present a GPU-accelerated method for large scale, coupled incompressible fluid flow and heat transfer problems. A high-order, nodal discontinuous Galerkin method is utilized to discretize governing equations on unstructured triangular meshes. A semi-implicit scheme with explicit treatment of the advective terms and implicit treatment of the split Stokes operators are used for time discretization. The pressure system is solved with a conjugate gradient method together with a fully GPU-accelerated multigrid preconditioner. The code is built on scalable libParanumal solver which is a library of high-performance kernels for high-order discretizations. Performance portability is achieved by using the open concurrent compute abstraction, OCCA. A set of numerical experiments including free and mixed convection problems indicate that our approach experimentally reaches design order of accuracy.

Sikiştirilamaz Isil Taşinim Problemleri̇ni̇n Fi̇zi̇kle Öğrenen Yapay Si̇ni̇r Ağlari İle Çözümü

“…Also, in Figure 4, the center line profiles of velocity and temperature for different Ra numbers are shown. These contours and profiles qualitatively match with the high order solutions (Karakus, 2022). To increase the accuracy, we changed the weights of different loss terms as Ra changes.…”

“…Hossain et al (2021) developed a spectral/hp element method for the Direct Numerical Simulation (DNS) of incompressible thermal convective flows by considering Boussinesq type thermal bodyforcing with periodic boundary conditions and enforcing a constant volumetric flow rate. In Karakus (2022), the author presented a GPU accelerated nodal discontinuous Galerkin method on unstructured triangular meshes for solving problems on different convective regimes.…”

Physics Informed Neural Networks for Two Dimensional Incompressible Thermal Convection Problems

“…Hossain et al (2021) developed a spectral/hp element method for the Direct Numerical Simulation (DNS) of incompressible thermal convective flows by considering Boussinesq type thermal body-forcing with periodic boundary conditions and enforcing a constant volumetric flow rate. In Karakus (2022), the author presented a GPU accelerated nodal discontinuous Galerkin method on unstructured triangular meshes for solving problems on different convective regimes. Apart from the traditional numerical methods such as finite difference, finite volume and finite element methods, data driven machine learning methods are used to solve the partial differential equations (PDE) (Willard et al, 2020).…”