Adaptive Mesh and Algorithm Refinement Using Direct Simulation Monte Carlo

Towards adaptive kinetic-fluid simulations of weakly ionized plasmas

Adaptive kinetic-fluid solvers for heterogeneous computing architectures

Summary An adaptive three-dimensional mesh refinement method based on the law of mass conservation has been introduced and tested using some analytical velocity fields as accurate in identifying singular point, asymptotic plane and drawing closed streamlines. This paper further investigates the adaptive mesh refinement method using a velocity field that is due to a uniform strain and a point vortex. Similar results have been obtained.

We describe the development and implementation of a block-based adaptive mesh refinement (AMR) algorithm for solving the discrete ordinates neutral particle transport equation. AMR algorithms allow mesh refinement in areas of interest without requiring the extension of this refinement throughout the entire problem geometry, minimizing the number of computational cells required for calculations. The block-based AMR algorithm described here is a hybrid between traditional cell or patch-based approaches and is designed to allow an efficient parallel solution of the transport equation while still reducing the cell count.This paper discusses the data structure implementation and CPU/memory efficiency for our Block AMR method, the equations and procedures used in mapping edge fluxes between blocks of different refinement levels for both diamond and linear discontinuous spatial discretizations, effects of AMR on mesh convergence, and our approach to parallelization. Comparisons between our Block AMR method and a traditional single-level mesh are presented for a sample brachytherapy problem. The Block AMR results are shown to be significantly faster for this problem (on at least a few processors), while still returning an accurate solution.

Aerodynamic heating in hypersonic flow presents one of the most serious challenges in the design of space vehicles. In the present study, heat flux reduction mechanism of the pulsed counterflowing jet from the nose of a blunt body is numerically investigated. Flow field around the hemisphere model is calculated in hypersonic free stream of Mach number 10 and Knudsen number 0.4. Considering that the external flow field is highly rarefied, recent works have demonstrated the direct simulation Monte Carlo (DSMC) technique to accurately predict the flow field under steady-state conditions. For supersonic flow with a counterflowing jet, the mean free path could vary by orders of magnitude within the computation domain and the computational mesh size in DSMC should be of one third of local mean free path (MFP) of the gas due to the requirement of selecting colliding partners among particles. Therefore, the open-source SPARTA code with octree Cartesian mesh is utilized in our research with Adaptive Mesh Refinement (AMR), which has been widely used in modern DSMC codes. AMR is crucial for efficient solutions of multi-scale problems characterized by large gradients of parameters in localized areas of the computational domain. Currently, tree-based methods have being developed for extremely large scale AMR simulations with billions of cells. As a conclusion, significant decreases of surface heat flux are obtained and counterflowing jet is proved to be effective on heat flux reduction in the vicinity of the stagnation point.

We present two cases where the adaptive mesh refinement (AMR) calculation can have larger error than that of uniform grid without AMR. The first one is for AMR calculation with locked time step, which uses the same small stepsize for all grid cells. The locked time step without subcycling on the fine mesh can lead to larger dispersion error than the coarse grid without AMR. The second one is for AMR calculation on cylindrical (r, z) coordinate. The reflection wave at the coarse-fine interface of AMR with several refinement levels can trigger shock instability, i.e., Carbuncle phenomenon, near the z-axis. In both cases, the AMR should be used cautiously.

A parallel implicit adaptive mesh refinement (AMR) algorithm is described for the system of partial-differential equations governing steady two-dimensional compressible gaseous flows. The AMR algorithm uses an upwind finite-volume spatial discretization procedure in conjunction with limited linear solution reconstruction and Riemann-solver based flux functions to solve the governing equations on multi-block mesh composed of structured curvilinear blocks with quadrilateral computational cells. A flexible block-based hierarchical data structure is used to facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. A Jacobian-free inexact Newton method is used to solve the system of nonlinear equations arising from this finite-volume spatial discretization procedure and a preconditioned generalized minimal residual (GMRES) method is used to solve the resulting non-symmetric system of linear equations at each step of the Newton algorithm. An additive Schwarz global preconditioner with variable overlap is used in conjunction with block-fill incomplete lower-upper (BFILU) type preconditioners based on the Jacobian of the first-order upwind scheme for each sub-domain. The Schwarz preconditioning and block-based data structure readily allow efficient and scalable parallel implementations of the implicit AMR approach on distributed-memory multi-processor architectures. Numerical results will be described for several flow cases, demonstrating both the effectiveness of the mesh adaptation and algorithm parallel performance. The proposed parallel implicit AMR method allows for anisotropic mesh refinement and is well suited for predicting complex flows with disparate spatial and temporal scales.

Development of an object-oriented finite element program with adaptive mesh refinement for multi-physics applications

A unified framework for the computational comparison of adaptive mesh refinement strategies for all-quadrilateral and all-hexahedral meshes: Locally adaptive multigrid methods versus h-adaptive methods

Robust adaptive mesh refinement for transonic conditions is one of the most difficult challenges to advancing CFD usage for certification by analysis. Transonic fluid-structure interaction cases represent an even more difficult challenge for adaptive mesh refinement. Production aircraft furthermore have structural models that have gaps and discontinuities that make the interdomain transfer of loads and deflections difficult. This adds to the challenge of adaptive mesh refinement. An initial attempt to create an adaptive mesh refinement process that refines regions of high flow gradient based around the HeldenMesh software is presented. The method is applied to the Integrated Adaptive Wing Technology Maturation (IAWTM) configuration. That has developed an aspect ratio 13.5 wing aeroelastic wind-tunnel model for testing in the Transonic Dynamics Tunnel (TDT). The high levels of deformation of this wing make the adaptation of meshes for the static shape difficult and has necessitated some creativity in how to efficiently adapt meshes. A time-domain identification of the unsteady system based on flexible modes using the adapted meshes is performed.

PurposeThe Hermite collocation method of discretization can be used to determine highly accurate solutions to the steady‐state one‐dimensional convection‐diffusion equation (which can be used to model the transport of contaminants dissolved in groundwater). This accuracy is dependent upon sufficient refinement of the finite‐element mesh as well as applying upstream or downstream weighting to the convective term through the determination of collocation locations which meet specified constraints. Owing to an increase in computational intensity of the application of the method of collocation associated with increases in the mesh refinement, minimal mesh refinement is sought. Very often this optimization problem is the one where the feasible region is not connected and as such requires a specialized optimization search technique. This paper aims to focus on this method.Design/methodology/approachAn original hybrid method that utilizes a specialized adaptive genetic algorithm followed by a hill‐climbing approach is used to search for the optimal mesh refinement for a number of models differentiated by their velocity fields. The adaptive genetic algorithm is used to determine a mesh refinement that is close to a locally optimal mesh refinement. Following the adaptive genetic algorithm, a hill‐climbing approach is used to determine a local optimal feasible mesh refinement.FindingsIn all cases the optimal mesh refinements determined with this hybrid method are equally optimal to, or a significant improvement over, mesh refinements determined through direct search methods.Research limitationsFurther extensions of this work could include the application of the mesh refinement technique presented in this paper to non‐steady‐state problems with time‐dependent coefficients with multi‐dimensional velocity fields.Originality/valueThe present work applies an original hybrid optimization technique to obtain highly accurate solutions using the method of Hermite collocation with minimal mesh refinement.

The development of turbulent vortical wakes released downstream of wind turbines is crucial as it presents many technological implications for wind farm design and exploitation. The numerical prediction of these wakes constitutes a challenging problem as they involve the shedding of fine vortical structures, their instabilities, and interactions with a turbulent ambient flow. A Large Eddy Simulation (LES) approach allows capturing such flow phenomena, which implies a suitable mesh. Adaptive Mesh Refinement (AMR) is used to refine the mesh in the wind turbine wake to limit the computational cost. A methodology is developed to define and capture the wake envelope adequately. Three main parts of this methodology can be identified: The wind turbine wake detection, the target cell size required and adaptation frequency. The target cell size needed to properly capture the wind turbine wake is investigated in previous work [1], while this paper focuses on wind turbine wake detection. A strategy based on a progress variable with a source term in the rotor region is used to capture the wake. This variable is transported by the flow and thus defines the wake envelope. AMR is used to refine the mesh within this region. To validate the method, a comparison between an adaptive mesh case and a reference mesh case has been performed on a single rotor and a two aligned rotor configuration. For both, the wind turbine wake tracking method is effective. The progress variable is transported correctly and leads to a well-defined wake area. The mesh is refined adequately within it. The physical comparison between cases showed similar results, while the performance comparison showed a computational cost reduction of 30% in the single turbine configuration and 50% in the two turbines configuration. Therefore, our methodology coupled with adaptive mesh refinement can adequately capture wind turbine wake, define an accurate wake envelope and decrease the computational cost for the same physical precision.

A new adaptive local mesh refinement algorithm and its application on fourth order thin film flow problem

Runtime data sharing across applications is of great importance for avoiding high I/O overhead for scientific data analytics. Sharing data on a staging space running on a set of dedicated compute nodes is faster than writing data to a slow disk-based parallel file system (PFS) and then reading it back for post-processing. Originally, the staging space has been purely based on main memory (DRAM), and thus was several orders of magnitude faster than the PFS approach. However, storing all the data produced by large-scale simulations on DRAM is impractical. Moving data from memory to SSD-based burst buffers is a potential approach to address this issue. However, SSDs are about one order of magnitude slower than DRAM. To optimize data access performance over the staging space, methods such as prefetching data from SSDs according to detected spatial access patterns and distributing data across the network topology have been explored. Although these methods work well for uniform mesh data, which they were designed for, they are not well suited for adaptive mesh refinement (AMR) data. Two mąjor issues must be addressed before constructing such a memory hierarchy and topology-aware runtime AMR data sharing framework: (1) spatial access pattern detection and prefetching for AMR data; (2) AMR data distribution across the network topology at runtime. We propose a framework that addresses these challenges and demonstrate its effectiveness with extensive experiments on AMR data. Our results show the framework's spatial access pattern detection and prefetching methods demonstrate about 26% performance improvement for client analytical processes. Moreover, the framework's topology-aware data placement can improve overall data access performance by up to 18%.

Quantitative 3D phase field modelling of solidification using next-generation adaptive mesh refinement