Mehmet Haluk Aksel

A GPU-accelerated adaptive discontinuous Galerkin method for level set equation

ABSTRACT This paper presents a GPU-accelerated nodal discontinuous Galerkin method for the solution of two- and three-dimensional level set (LS) equation on unstructured adaptive meshes. Using adaptive mesh refinement, computations are localised mostly near the interface location to reduce the computational cost. Small global time step size resulting from the local adaptivity is avoided by local time-stepping based on a multi-rate Adams–Bashforth scheme. Platform independence of the solver is achieved with an extensible multi-threading programming API that allows runtime selection of different computing devices (GPU and CPU) and different threading interfaces (CUDA, OpenCL and OpenMP). Overall, a highly scalable, accurate and mass conservative numerical scheme that preserves the simplicity of LS formulation is obtained. Efficiency, performance and local high-order accuracy of the method are demonstrated through distinct numerical test cases.

A GPU accelerated level set reinitialization for an adaptive discontinuous Galerkin method

GPU accelerated high order reconstruction of signed distance function of the level set method is studied. The flow based reinitialization equation is discretized in space by using a nodal discontinuous Galerkin method on adaptive unstructured grids. Artificial diffusion with a modal decay rate based regularity estimator is used to damp out high frequency solution components near kinks, where mesh adaptivity is applied. A two rate Adams-Bashforth time integrator is developed to avoid time step restrictions resulting from artificial diffusion stabilization and local mesh refinement. Platform independence of the solver is achieved by using an extensible multi-threading programming API that allows runtime selection of different computing devices (GPU and CPU) and threading interfaces (CUDA, OpenCL and OpenMP). Overall, a highly scalable numerical scheme that preserves the simplicity of the original level set method is obtained. Performance and accuracy of the method to construct signed distance function on highly disturbed initial data with smooth and non-smooth interfaces are tested through distinct two- and three-dimensional problems.

Lift coefficient calculation using a geometric/solution adaptive Navier Stokes solver on two-dimensional cartesian grids for compressible and turbulent flows

In this study, two-dimensional geometric and solution adaptive refinement/coarsening scheme codes are generated by the use of Cartesian grid generation techniques. In the solution of compressible, turbulent flows one-equation Spalart-Allmaras turbulence model is implemented. The performance of the flow solver is tested on the case of high Reynolds number, steady flow around NACA 0012 airfoil. The lift coefficient solution for the airfoil at a real-life-flight Reynolds number is compared with the experimental study in literature.

BOEING TR-1322 Çoklu-elemanlı Kanat Profili Çevresinde Sıkıştırılabilir Akış için Çözüm Uyarlamalı Kartezyen Ağ Temelli Euler Çözümü

Kartezyen aglar yapisal olmayan ag teknolojisi icinde ozel bir dal olusturmaktadir. Karmasik geometriler icin otomatik ag olusturmak ve bu gibi geometriler etrafinda akisin govde seklinden ve sayisindan bagimsiz sekilde benzetim kurmak icin ozellikle tasarlanmis algoritmalar kullanirlar. Kartezyen aglar, Kartezyen hucrelerinin birbirlerine baglanmalarini saglamak icin olusturulan dortlu agac temelli veri yapisi kullanarak uretilmistir. GeULER isimli, kullanici mudahalesine gerek olmayan, nesne tabanli FORTRAN programlama dilinde Kartezyen ag ureticisi temelli Euler cozumu uygulanmistir. Bu calismada, gelistirilen sikistirilabilir akis cozucusune, BOEING TR-1322 coklu-elemanli kanat profili cevresinde kesik hucre uyarlamasi ve egri uyarlamasi gibi ozel Kartezyen temelli algoritmalar kullanilarak iki-boyutlu uyarlanabilir gelistirme/genisleme sema kodlari ilave edilmistir. Kanat profili uzerinde, 0.11 serbest akim Mach sayisinda, ses alti akista kanat cevresindeki basinc dagiliminin tahmini icin test edilmis ve gelistirilen GeULER kodu kullanilarak akisin Mach konturlari tasvir edilmistir

Octree Based 3-D Unstructured Grid Coarsening and Multigrid Viscous Flow Solutions

In this study, a new grid coarsening method based on localization of the grid cells on an octree data structure is developed for multigrid applications. Three dimensional unstructured / hybrid grid cells are agglomerated via octree data structure to obtain coarse grid levels. It is shown that, the octree based cell agglomeration and grid coarsening method developed provides well defined, nested, body fitted coarser grid cells with an aspect ratio of about one at all coarse grid levels. Several multigrid cycling algorithms are adapted to a viscous flow solver, SENSE3D, developed at TUBITAK-SAGE and flow solutions are presented for inviscid / viscous flow cases. An inviscid flow solution over an ONERA M6 wing and a laminar flow solution over a NACA0012 Airfoil are presented. The convergence accelerations obtained are about 8 times for low speed inviscid flows, and in the range of 4 to 13 times for laminar flows.