Direct immersogeometric fluid flow analysis using B-rep CAD models

We present a new method for immersogeometric fluid flow analysis that directly uses the CAD boundary representation (B-rep) of a complex object and immerses it into a locally refined, non-boundary-fitted discretization of the fluid domain. The motivating applications include analyzing the flow over complex geometries, such as moving vehicles, where the detailed geometric features usually require time-consuming, labor-intensive geometry cleanup or mesh manipulation for generating the surrounding boundary-fitted fluid mesh. The proposed method avoids the challenges associated with such procedures. A new method to perform point membership classification of the background mesh quadrature points is also proposed. To faithfully capture the geometry in intersected elements, we implement an adaptive quadrature rule based on the recursive splitting of elements. Dirichlet boundary conditions in intersected elements are enforced weakly in the sense of Nitsche\u27s method. To assess the accuracy of the proposed method, we perform computations of the benchmark problem of flow over a sphere represented using B-rep. Quantities of interest such as drag coefficient are in good agreement with reference values reported in the literature. The results show that the density and distribution of the surface quadrature points are crucial for the weak enforcement of Dirichlet boundary conditions and for obtaining accurate flow solutions. Also, with sufficient levels of surface quadrature element refinement, the quadrature error near the trim curves becomes insignificant. Finally, we demonstrate the effectiveness of our immersogeometric method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of an agricultural tractor directly represented using B-rep

A geometric framework for immersogeometric analysis

The purpose of this dissertation is to develop a geometric framework for immersogeometric analysis that directly uses the boundary representations (B-reps) of a complex computer-aided design (CAD) model and immerses it into a locally refined, non-boundary-fitted discretization of the fluid domain. Using the non-boundary-fitted mesh which does not need to conform to the shape of the object can alleviate the challenge of mesh generation for complex geometries. This also reduces the labor-intensive and time-consuming work of geometry cleanup for the purpose of obtaining watertight CAD models in order to perform boundary-fitted mesh generation. The Dirichlet boundary conditions in the fluid domain are enforced weakly over the immersed object surface in the intersected elements. The surface quadrature points for the immersed object are generated on the parametric and analytic surfaces of the B-rep models. In the case of trimmed surfaces, adaptive quadrature rule is considered to improve the accuracy of the surface integral. For the non-boundary-fitted mesh, a sub-cell-based adaptive quadrature rule based on the recursive splitting of quadrature elements is used to faithfully capture the geometry in intersected elements. The point membership classification for identifying quadrature points in the fluid domain is based on a voxel-based approach implemented on GPUs. A variety of computational fluid dynamics (CFD) simulations are performed using the proposed method to assess its accuracy and efficiency. Finally, a fluid--structure interaction (FSI) simulation of a deforming left ventricle coupled with the heart valves shows the potential advantages of the developed geometric framework for the immersogeomtric analysis with complex moving domains

An improved impermeable solid boundary scheme for the MLPG_R method and a two-phase ISPH model for suspended sediment-laden flows

Over the past decades, meshless methods have become an essential numerical tool for simulating a wide range of science and engineering problems. The key idea of the meshless methods is to provide accurate and stable numerical solutions, where the computation domain is discretized using particles instead of using conventional meshes. In this thesis, developments on the Meshless Local Petrov-Galerkin (MLPG) method and incompressible smoothed particle hydrodynamics (ISPH) have been carried out for rigid boundary condition implementation and simulation of dispersed two-phase flows, respectively. For rigid boundary condition implementation in the MLPG method, an improved boundary scheme is developed through a weak formulation for the boundary particles based on Pressure Poisson Equation (PPE). In this scheme, the wall boundary particles simultaneously satisfy the PPE in the local integration domain by adopting the MLPG method with the Rankine source solution (MLPG_R) integration scheme (Ma, 2005b) and the pressure Neumann boundary condition. The new weak formulation vanishes the derivatives of the unknown pressure at wall particles and is discretized in the truncated support domain without extra artificial treatment. This improved boundary scheme is validated by analytical solutions, numerical benchmarks, and experimental data in the cases of patch tests, lid-driven cavity, flow over a cylinder and monochromic wave generation. The numerical results show higher accuracy in pressure and velocity, especially near the boundary, compared to the existing boundary treatment methods that directly discretize the pressure Neumann boundary condition. For two-phase meshless model development, the incompressible SPH method is developed for simulating suspended sediment transport problems. The fluid and sediment are treated as two continuous phases described by two sets of Navier-Stokes equations with interactions between two phases achieved by the drag force. The computational domain is discretized into a single set of SPH particles which move with the fluid velocity but carry the local properties of both phases, including sediment velocity and its volume fraction. In addition, large eddy simulation (LES) is employed for representing the turbulent effect, in which the eddy viscosities are defined by the Smagorinsky model. The pressure Neumann boundary condition is imposed on the rigid solid walls and the zero pressure boundary condition on the free water surface. The two-phase model is verified by the analytical solutions for two idealized problems of still water with neutrally buoyant sediment and still water with naturally settling sediment in a two-dimensional water tank. The model is then applied to the study of sand dumping. It is shown that the characteristics of the settling sand cloud, the pressure field, and the flow vortices are in good agreement with experimental results. The proposed two-phase model is proven to be effective for the numerical study of suspended sediment problems