101st NIA CFD Seminar Webcast: Meshless Methods for the Neutron Transport Equation by Brody Bassett

April 23, 2018 - Leave a Response

101st NIA CFD Seminar

Topic: Meshless Methods for the Neutron Transport Equation

Date: Wednesday, May 02, 2018

Time: 10am-11am (EST)

Room: NIA, Rm137

Speaker: Brody Bassett

Speaker Bio: Brody Bassett received his BS in Physics from Brigham Young University and his MS in Nuclear Engineering from Oregon State University. He is currently working on his Ph.D. in Nuclear Engineering and Radiological Sciences at the University of Michigan, where his dissertation is focused on the application of meshless methods to the neutron transport equation.

Abstract: Mesh-based methods for the numerical solution of partial differential equations (PDEs) require the division of the problem domain into non-overlapping, contiguous subdomains that conform to the problem geometry. The mesh constrains the placement and connectivity of the solution nodes over which the PDE is solved. In meshless methods, the solution nodes are independent of the problem geometry and do not require a mesh to determine connectivity. This allows the solution of PDEs on geometries that would be difficult to represent using even unstructured meshes. The ability to represent difficult geometries and place solution nodes independent of a mesh motivates the use of meshless methods for the neutron transport equation, which often includes spatially-dependent PDE coefficients and strong localized gradients. The meshless local Petrov-Galerkin (MLPG) method is applied to the steady-state and k-eigenvalue neutron transport equations, which are discretized in energy using the multigroup approximation and in angle using the discrete ordinates approximation. The MLPG method uses weighted residuals of the transport equation to solve for basis function expansion coefficients of the neutron angular flux. Connectivity of the solution nodes is determined by the shared support domain of overlapping meshless functions, such as radial basis functions (RBFs) and moving least squares (MLS) functions.

To prevent oscillations in the neutron flux, the MLPG transport equations are stabilized by the streamline-upwind Petrov-Galerkin (SUPG) method, which adds numerical diffusion to the streaming term. Global neutron conservation is enforced by using MLS basis and weight functions and appropriate SUPG parameters. The cross sections in the transport equation are approximated in accordance with global particle balance and without constraint on their spatial dependence or the location of the basis and weight functions. The equations for the strong-form meshless collocation approach are derived for comparison to the MLPG equations. Two integration schemes for the basis and weight functions in the MLPG method are presented, including a background mesh integration and a fully meshless integration approach. The method of manufactured solutions (MMS) is used to verify the resulting MLPG method in one, two and three dimensions. Results for realistic problems, including two-dimensional pincells, a reflected ellipsoid and a three-dimensional problem with voids, are verified by comparison to Monte Carlo simulations. Finally, meshless heat transfer equations are derived using a similar MLPG approach and verified using the MMS. These heat equations are coupled to the MLPG neutron transport equations and results for the power coefficient of reactivity are compared to values from a commercial pressurized water reactor.

Additional information, including the webcast link, can be found at the NIA CFD Seminar website:


TODAY: 100th NIA CFD Seminar Webcast: Uses of Zero and Negative Volume Elements for Node-Centered Edge-Based Discretization by Hiroaki Nishikawa

April 10, 2018 - Leave a Response

100th NIA CFD Seminar

Topic: Uses of Zero and Negative Volume Elements for Node-Centered Edge-Based Discretization

Date: Tuesday, April 10, 2018

Time: 11am-noon (EST)

Room: NIA, Rm101

Speaker: Hiroaki Nishikawa

Speaker Bio: Dr. Hiro Nishikawa is Associate Research Fellow, NIA. He earned Ph.D. in Aerospace Engineering and Scientific Computing at the University of Michigan in 2001. He then worked as a postdoctoral fellow at the University of Michigan on adaptive grid methods, local preconditioning methods, multigrid methods, rotated-hybrid Riemann solvers, high-order upwind and viscous schemes, and joined NIA in 2007. His area of expertise is the algorithm development for CFD, focusing on the hyperbolic method for diffusion, and derived methods for robust, efficient, highly accurate viscous discretization schemes on unstructured grids.

Abstract: This talk will discuss how zero and negative volume elements can be useful in Computational Fluid Dynamics (CFD) simulations: third-order accuracy on grids with inverted triangles, singularities better resolved with zero volume elements, zero-width shock capturing, local refinement of quadrilateral grids without hanging nodes, overset grids made a single grid for a drastic simplification in algorithms and for trivial satisfaction of discrete conservation. All practical CFD codes in the world today consider grids with zero/negative volumes as invalid or failure, and thus simulations are never performed on such grids. This work opens the door to a new era in CFD: improved simulations via hitherto-impossible computational grids.

Additional information, including the webcast link, can be found at the NIA CFD Seminar website: