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+---
+contributor: max
+date: '2024-12-19T09:43:10'
+title: 'Implementation of Two Numerical Solvers for the Study of Non-Equilibrium Gas Dynamics on GPU-Accelerated Platforms using SYCL'
+external_url: 'https://ruor.uottawa.ca/items/cb39b8e3-9904-4a65-89bf-5414d364e759'
+authors:
+  - El-Ghotmi, Osman
+tags:
+  - sycl
+  - gpu
+  - portability
+---
+
+The application of GPUs has extended beyond traditional graphics rendering because their
+parallel processing capabilities can accelerate many general-purpose tasks, such as machine
+learning and scientific computing. This thesis presents the implementation of two numerical
+solvers for the solution of non-equilibrium gas flows. It also demonstrates the computational
+performance of the two solvers when developed to target GPU-based supercomputers using the SYCL
+programming model. The first solver incorporates a novel ray-tracing technique and accurate
+mathematical relations to efficiently compute any observable property of free-molecular flow
+past convex shapes (FMFC). It computes integrals of the Maxwell-Boltzmann distribution function
+to create an algorithm that quickly evaluates any moment of the local particle-velocity
+distribution. This highly efficient technique is extended for GPUs to accelerate the
+computation of accurate results. Results produced with the solver serve as robust benchmarks
+in the validation of other scientific models that describe fluid motion in non-equilibrium
+regimes. The second solver extends a CPU-based implementation of the discontinuous Galerkin Hancock (DGH)
+method into an efficient GPU code. The DGH scheme is a high-order numerical method that
+solves hyperbolic partial differential equations (PDEs) with stiff source terms. This class
+of equations is common in many models that are used to describe non-equilibrium gas flows.
+The GPU implementation of the DGH solver that is presented in this work provides a
+computationally efficient and numerically accurate method to compute the solution for these
+models. Results produced by the FMFC and DGH solvers showcase their accuracy and parallel
+scalability as efficient GPU algorithms. Furthermore, the effectiveness of the FMFC
+solver as a validation tool is demonstrated by producing benchmarks to confirm the
+accuracy of scientific models that are solved with numerical schemes such as DGH.