Coarse grid projection (CGP) methodology is a novel multigrid method for systems involving decoupled nonlinear evolution equations and linear elliptic Poisson equations. The nonlinear equations are solved on a fine grid and the linear equations are solved on a corresponding coarsened grid. Mapping operators execute data transfer between the grids. The CGP framework is constructed upon spatial and temporal discretization schemes. This framework has been established for finite volume/difference discretizations as well as explicit time integration methods. In this article we present for the first time a version of CGP for finite element discretizations, which uses a semi-implicit time integration scheme. The mapping functions correspond to the finite-element shape functions. With the novel data structure introduced, the mapping computational cost becomes insignificant. We apply CGP to pressure correction schemes used for the incompressible Navier Stokes flow computations. This version is validated on standard test cases with realistic boundary conditions using unstructured triangular meshes. We also pioneer investigations of the effects of CGP on the accuracy of the pressure field. It is found that although CGP reduces the pressure field accuracy, it preserves the accuracy of the pressure gradient and thus the velocity field, while achieving speedup factors ranging from approximately 2 to 30. Exploring the influence of boundary conditions on CGP, the minimum speedup occurs for velocity Dirichlet boundary conditions, while the maximum speedup occurs for open boundary conditions. We discuss the CGP method as a guide for partial mesh refinement of incompressible flow computations and show its application for simulations of flow over a backward facing step and flow past a cylinder. / Master of Science

In this thesis, an innovative coarse grid CFD approach is developed that aims toexploit the capabilities of sub-channel codes and CFD methods while overcoming theirlimitations. In the approach, a very coarse mesh is implemented in the CFD softwareOpenFOAM and a new wall treatment, based on the traditional concept of the wallfunction, is applied to the wall boundary conditions of the domain to take into accountthe low resolution of the grid which does not allow to effectively capture the effect of thesolid walls on the thermo-hydraulics of the flow. To investigate the performance of thenew approach, the method is implemented first in three simple test cases for whichthe sub-channel codes are the state-of-the-art thermo-hydraulic analysis since theyare single-phase flow problems in which there are no prevailing 3D flow conditions.An additional test case representing a 2x2 fuel bundle with three full-length rods andone half-length rod is investigated to verify the behavior of the new approach in caseswhere secondary flows are present. The results for the pressure fields are comparedwith the analytical pressure profiles for the four test cases that well represent the onesthat would be obtained with sub-channel code analysis, while the results for the wallshear stresses obtained in the four test cases are compared with the ones obtained witha more refined mesh in which the traditional wall function approach is implementedsince they should be the best estimation of the actual wall shear stresses at the walldomain. For the first two cases, the developed approach produces reasonable resultswith a good agreement to the analytical pressure profiles while the other two testcases show that the methodology has a limited applicability and, before proceedingwith the extension of the new approach to single-phase problems with 3D prevailingphenomena and two-phase problems, it is necessary to solve the issues that emerge forsome types of cases. / I denna avhandling utvecklas en innovativ CFD-metod med grovt rutnät som syftar till att utnyttja kapaciteten hos underkanalskoder och CFD-metoder och samtidigt övervinna deras begränsningar. I metoden implementeras ett mycket grovt nät i CFD-programvaran OpenFOAM och en ny väggbehandling, baserad på det traditionella konceptet med vägg väggfunktion, tillämpas på domänens vägggränsvillkor för att ta hänsyn till den låga upplösningen av nätet som inte tillåter att effektivt fånga effekten av de solida väggar på flödets termo-hydraulik. För att undersöka prestandan hos den nya tillvägagångssättet implementeras metoden först i tre enkla testfall för vilka subkanalskoderna är den senaste termo-hydrauliska analysen eftersom de är enfasflödesproblem där det inte finns några rådande 3D-flödesförhållanden.Ett ytterligare testfall som representerar ett 2x2 bränsleknippe med tre fullängdsstavar och en halvlång stav undersöks för att verifiera beteendet hos den nya metoden i fall där sekundära flöden förekommer. Resultaten för tryckfälten jämförs med de analytiska tryckprofilerna för de fyra testfall som väl representerar de som som skulle erhållas med kodanalys av underkanalen, medan resultaten för väggskjuvspänningarna skjuvspänningar som erhållits i de fyra testfallen jämförs med de som erhållits med ett mer förfinat nät i vilket den traditionella väggfunktionsmetoden är implementerad eftersom de bör vara den bästa uppskattningen av de faktiska väggskjuvspänningarna vid väggens domän. För de två första fallen ger den utvecklade metoden rimliga resultat med en god överensstämmelse med de analytiska tryckprofilerna medan de andra två visar att metoden har en begränsad tillämplighet och, innan man går vidare med utvidgningen av den nya metoden till enfasproblem med 3D-fenomen och två fenomen och tvåfasproblem, är det nödvändigt att lösa de problem som uppstår för vissa vissa typer av fall.

A new method for the determination of finely-gridded reservoir simulation pressures has been developed. It is estimated to be as much as hundreds to thousands of times faster than other methods for very large reservoir simulation grids. The method extends the work of Weber et al. Weber demonstrated accuracies for the pressure solution normally requiring millions of cells using traditional finite-difference equations with only hundreds of cells. This was accomplished through the use of finite-difference equations that incorporate the physics of the flow. Although these coarse-grid solutions achieve accuracies normally requiring orders of magnitude more resolution, their coarse resolution does not resolve local pressure variations resulting from fine-grid permeability variations. Many oil reservoir simulation models require fine grids to adequately represent the reservoir properties. Weber's coarse grids are of little value. This study takes advantage of the accurate coarse-grid solutions of Weber, by nesting them in the requisite fine grids to achieve much faster solutions of the large systems. Application of the nested-grid method involved calculating an accurate solution on a coarse grid, nesting the coarse-grid solution as fixed points into a finer grid and solving. Best results were obtained when an optimal number of coarse-grid pressure points were nested into the fine grid and when an optimal number of nested-grid systems were used.