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Showing 1 to 17 of 17 for “"Manufactured Solutions"”.
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Modified nodal integral method for non-linear coupled neutronics-heat conduction problems and exact solutions based on method of manufactured solutions
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01
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Verification of Compressible and Incompressible Computational Fluid Dynamics Codes and Residual-based Mesh Adaptation
… surfaces is proposed for easier generation of manufactured solutions during the verification of certain boundary conditions involving many constraints. To perform rigorous code verification, general grids with mixed cell types at the verified boundary are used. A novel approach is introduced to …
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CPU/GPU Code Acceleration on Heterogeneous Systems and Code Verification for CFD Applications
… model implementation using the method of manufactured solutions and code-to-code comparisons. First, a variety of performance optimizations both agnostic and specific to applications and platforms are developed in order to 1) improve the heterogeneous CPU/GPU compute utilization; 2) …
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Code Verification and Numerical Accuracy Assessment for Finite Volume CFD Codes
… Dynamics (CFD) code is performed. The Method of Manufactured Solutions is used to generate exact solutions for the Euler and Navier-Stokes equations to verify the correctness of the code through order of accuracy testing. The verification testing is performed on different mesh types which include …
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Analysis and implementation of a high-order reconstruction algorithm for an unstructured finite volume flow solver
… limitations by computing comparable solutions on grids that are coarser than grids required by a second-order flow solver. The scheme was chosen based on two criteria. The first being that it is well documented in the literature for two-dimensional flow solvers. The second is that the …
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Coupled radiation transport and mobile depletion for health physics and environmental impact applications
… solver is then verified with the method of manufactured solutions. The coupled solvers are then used to analyze the formation of ⁴¹Ar in a containment volume due to ex-core neutron fields, and the photon fields from a ¹³⁷Cs plume. The conclusions of this work indicate that these methods are …
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Stabilized finite elements for compressible turbulent Navier-Stokes
… methodology is used to obtain steady state solutions or to drive unsteady problems at each time step. Order of accuracy is assessed for inviscid and viscous flows in two and three dimensions via the method of manufactured solutions. Proper treatment of curved surface geometries is of vital …
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Numerical Approximation of Multiphase Flows in Heterogeneous Porous Media
… of numerical tests ranging from method of manufactured solutions, the quarter five-spot problem, and viscous fingering generation. The result is a robust convergent scheme achieving optimal levels of convergence to both small and large-scale problems. Furthermore, the scheme provides …
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Viscoelastic Fluid Modeling for Geophysical Applications in an Eulerian Framework
… and validation, including the method of manufactured solutions, reveal challenges in achieving mesh-convergent solutions under uniform refinement. Finally, we compare the proposed models against classical viscoelastic benchmark problems, providing insight into the effects of modeling and …
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Analysis of Plane Strain Deformations of Linearly Elastic Strain-Gradient Materials by the Finite Element Method
… displacements compare well with the analytical solutions available in the literature, thus verifying the numerical solution. The Method of Manufactured solutions (MMS) was used to further verify the developed code as the assumed displacements and the resulting stresses were successfully …
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A stabilized finite element dynamic overset method for the Navier-Stokes equations
… A novel hole cutting procedure based on solutions to Poisson equation is introduced and compared to existing techniques. A MPI-based parallel three-dimensional overset grid assembly framework is developed. Order of accuracy is examined via the method of manufactured solutions. The …
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A stabilized finite element dynamic overset method for the Navier-Stokes equations
… A novel hole cutting procedure based on solutions to Poisson equation is introduced and compared to existing techniques. A MPI-based parallel three-dimensional overset grid assembly framework is developed. Order of accuracy is examined via the method of manufactured solutions. The …
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A multilevel method for meshless solution of the poisson equation in heat transfer and fluid flow
… equation in three model geometries, using manufactured solutions. Rapid convergence of the residual is observed with Dirichlet boundary conditions using Successive Over-Relaxation(SOR) as the relaxation scheme . However, convergence is seen to be quite modest for the all-Neumann boundary …
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Application of Improved Truncation Error Estimation Techniques to Adjoint Based Error Estimation and Grid Adaptation
Numerical solutions obtained through the use of Computational Fluid Dynamics (CFD) are subject to discretization error, which is locally generated by truncation error. The discretization error is extremely difficult to properly estimate and this in turn leads to uncertainty over the quality of the …
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Discretization Error Estimation and Exact Solution Generation Using the 2D Method of Nearby Problems
… Problems as a way to generate analytical exact solutions to problems governed by partial differential equations (PDEs). The method involves generating a numerical solution to the original problem of interest, curve fitting the solution, and generating source terms by operating the governing PDEs …
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The dynamic soil structure interaction of shallow foundations on dry sand beds
… has to be isolated from the shaking through manufactured damping systems or designed to withstand the full force of the dynamic shaking while the energy is dissipated through structural damping. There is, however, an increasing focus on reducing the coupling between the soil and foundation …