Cartesian Mesh Generation Research Articles

An efficient Cartesian mesh generation strategy for complex geometries

Cartesian meshes based on the immersed boundary method are widely adopted for their convenience in implementing automated mesh generation. The performance of Cartesian mesh generation, particularly for complex geometries, is a crucial factor that directly impacts the efficiency of computational fluid dynamics solutions. In this study, we present an innovative strategy for efficient Cartesian mesh generation. Our methodology centers around the inner product test (IPT), enabling precise and efficient interior/exterior determination for intersected Cartesian cells. For this purpose, we enhance the k-d tree based intersection determination process to provide essential information of surface mesh for IPT, while concurrently improving the efficiency of the determination process. Our new methods offer automatic generation capabilities for arbitrary complex geometries. Through a series of tests, the new methods illustrate the notable performance improvements with the generation time of less than 4 min for the Cartesian mesh with 108 cells. Overall, our work optimizes Cartesian mesh generation for complex geometries, presenting significant potential for addressing the challenges of moving boundary problems.

Cartesian Mesh Generation with Local Refinement for Immersed Boundary Approaches

In this paper, an efficient and robust Cartesian Mesh Generation with Local Refinement for an Immersed Boundary Approach is proposed, whose key feature is the capability of high Reynolds number simulations by the use of wall function models, bypassing the need for accurate boundary layer discretization. Starting from the discrete manifold model of the object to be analyzed, the proposed model generates Cartesian adaptive grids for a CFD simulation, with minimal user interactions; the most innovative aspect of this approach is that the automatic generation is based on the segmentation of the surfaces enveloping the object to be analyzed. The aim of this paper is to show that this automatic workflow is robust and enables to get quantitative results on geometrically complex configurations such as marine vehicles. To this purpose, the proposed methodology has been applied to the simulation of the flow past a BB2 submarine, discretized by non-uniform grid density. The obtained results are comparable with those obtained by classical body-fitted approaches but with a significant reduction of the time required for the mesh generation.

A Three-Dimensional Cartesian Mesh Generation Algorithm Based on the GPU Parallel Ray Casting Method

Robust and efficient Cartesian mesh generation for large-scale scene is of great significance for fluid dynamics simulation and collision detection. High-quality and large-scale mesh generation task in a personal computer is hard to achieve. In this paper, a parallel Cartesian mesh generation algorithm based on graphics processing unit (GPU) is proposed. The proposed algorithm is optimized based on the traditional ray casting method in computer graphics, and is more efficient and stable for large-scale Cartesian mesh generation. In the process of mesh generation, the geometries represented by triangular facets are transformed into a mesh composed of orthogonal hexahedrons. A parallel ray generation method is proposed to reduce the data exchange between the host memory and device memory. A parallel primitives searching method based on lattice grid is adopted to search the triangular facets for intersection calculation between rays and triangles. The parallel Cartesian mesh generation algorithm has been implemented using CUDA library. The performance of parallel Cartesian mesh generation algorithm has been promoted enormously compared with the traditional the sequential algorithm, which is shown in different numerical experiments. Through some tests, the performance of parallel algorithm is analyzed, and the results show that the parallel computing power of the GPU is fully utilized. Finally, examples of Cartesian mesh generation are presented.

Automatic off-body overset adaptive Cartesian mesh method based on an octree approach

This paper describes a method for generating adaptive structured Cartesian grids within a near-body/off-body mesh partitioning framework for the flow simulation around complex geometries. The off-body Cartesian mesh generation derives from an octree structure, assuming each octree leaf node defines a structured Cartesian block. This enables one to take into account the large scale discrepancies in terms of resolution between the different bodies involved in the simulation, with minimum memory requirements. Two different conversions from the octree to Cartesian grids are proposed: the first one generates Adaptive Mesh Refinement (AMR) type grid systems, and the second one generates abutting or minimally overlapping Cartesian grid set. We also introduce an algorithm to control the number of points at each adaptation, that automatically determines relevant values of the refinement indicator driving the grid refinement and coarsening. An application to a wing tip vortex computation assesses the capability of the method to capture accurately the flow features.

A discontinuous Galerkin method for solutions of the Euler equations on Cartesian grids with embedded geometries

We present a discontinuous Galerkin method (DGM) for solutions of the Euler equations on Cartesian grids with embedded geometries. Cartesian grid methods can provide considerable computational savings for computationally intensive schemes like the DGM. Cartesian mesh generation is also simplified compared to the body fitted meshes. However, cutting an embedded geometry out of the grid creates cut cells. These are difficult to deal with for two reasons: the restrictive CFL number and irregular shapes. Both of these issues are more involved for the DG than for finite volume methods, which most Cartesian grid techniques have been developed for. We use explicit time integration employing cell merging to avoid restrictively small time steps. We provide an algorithm for splitting complex cells into triangles and use standard quadrature rules on these for numerical integration. To avoid the loss of accuracy due to straight sided grids, we employ the curvature boundary conditions. We provide a number of computational examples for smooth flows to demonstrate the accuracy of our approach.

Trillion Cell CAD-Based Cartesian Mesh Generator for the Finite-Difference Time-Domain Method on a Single-Processor 4-GB Workstation

In this paper, a robust, computer-aided design (CAD)-based, highly accurate and fast Cartesian mesh generation technique for a colossal number of cells capacity using a minimal single-processor computing resource is presented. The cells are generated in Yee format for the finite-difference time-domain (FDTD) method. There are three key techniques presented that achieve this capability: a highly efficient data storage ray tracing method, a highly accurate ray-facet intersection test, and a novel exact arithmetic tie-breaking algorithm for rays intersecting facet edges and vertices.

Efficient and Robust Cartesian Mesh Generation for Building-Cube Method

In this study, an efficient and robust Cartesian mesh generation method for Building-Cube Method (BCM) is proposed. It can handle “dirty” geometry data whose surface has cracks, overlaps, and reverse of triangle. BCM mesh generation is implemented by two procedures; cube generation and cell generation in each cube. The cell generation procedure in this study is managed in each cube individually, and parallelized by OpenMP. Efficiency of the parallelized BCM mesh generation is demonstrated for several three-dimensional test cases using a multi-core PC.

Robust and Efficient Cartesian Mesh Generation for Component-Based Geometry

This work documents a new method for rapid and robust Cartesian mesh generation for component-based geometry. The new algorithm adopts a novel strategy that first intersects the components to extract the wetted surface before proceeding with volume mesh generation in a second phase. The intersection scheme is based on a robust geometry engine that uses adaptive precision arithmetic and automatically and consistently handles geometric degenerades with an algorithmic tie-breaking routine. The intersection procedure has worst-case computational complexity of O(N log N) and is demonstrated on test cases with up to 121 overlapping and intersecting components, including a variety of geometric degeneracies. The volume mesh generation takes the intersected surface triangulation as input and generates the mesh through cell division of an initially uniform coarse grid. In refining hexagonal cells to resolve the geometry, the new approach preserves the ability to directionally divide cells that are well aligned with local geometry. The mesh generation scheme has linear asymptotic complexity with memory requirements that total approximately 14-17 words/cell. The mesh generation speed is approximately 10 6 cells/minute on a typical engineering workstation

Robust and efficient Cartesian mesh generation for component-based geometry

Robust and efficient Cartesian mesh generation for component-based geometry