Implementation aspects of sequential Gaussian simulation on irregular points

CO 2 emissions and heat flow through soil, fumaroles, and steam heated mud pools at the Reykjanes geothermal area, SW Iceland

The objective of the Cranked-Arrow Wing Aerodynamics Project International (CAWAPI) was to allow a comprehensive validation of Computational Fluid Dynamics methods against the CAWAP flight database. A major part of this work involved the generation of high-quality computational grids. Prior to the grid generation an IGES file containing the air-tight geometry of the F-16XL aircraft was generated by a cooperation of the CAWAPI partners. Based on this geometry description both structured and unstructured grids have been generated. The baseline structured (multi-block) grid (and a family of derived grids) has been generated by the National Aerospace Laboratory NLR. Although the algorithms used by NLR had become available just before CAWAPI and thus only a limited experience with their application to such a complex configuration had been gained, a grid of good quality was generated well within four weeks. This time compared favourably with that required to produce the unstructured grids in CAWAPI. The baseline all-tetrahedral and hybrid unstructured grids has been generated at NASA Langley Research Center and the USAFA, respectively. To provide more geometrical resolution, trimmed unstructured grids have been generated at EADS-MAS, the UTSimCenter, Boeing Phantom Works and KTH/FOI. All grids generated within the framework of CAWAPI will be discussed in the article. Both results obtained on the structured grids and the unstructured grids showed a significant improvement in agreement with flight test data in comparison with those obtained on the structured multi-block grid used during CAWAP.

In this paper we focus on the application of a higher-order finite volume method for the resolution of Computational Aeroacoustics problems. In particular, we present the application of a finite volume method based in Moving Least Squares approximations in the context of a hybrid approach for low Mach number flows. In this case, the acoustic and aerodynamic fields can be computed separately. We focus on two kinds of computations: turbulent flow and aeroacoustics in complex geometries. Both fields require very accurate methods to capture the fine features of the flow, small scales in the case of turbulent flows and very low-amplitude acoustic waves in the case of aeroacoustics. On the other hand, the use of unstructured grids is interesting for real engineering applications, but unfortunately, the accuracy and efficiency of the numerical methods developed for unstructured grids is far to reach the performance of those methods developed for structured grids. In this context, we propose the FV-MLS method as a tool for accurate CAA computations on unstructured grids.

A Multiscale Control Volume framework using the Multiscale Restriction Smooth Basis and a non-orthodox Multi-Point Flux Approximation for the simulation of two-phase flows on truly unstructured grids

The traditional classical sampling statistics method ignores the spatial location relationship of survey samples, which leads to many problems. This study aimed to propose a spatial sampling method for sampling estimation and optimization of forest biomass, achieving a more efficient and effective monitoring system. In this paper, we used Sequential Gaussian Conditional Simulation (SGCS) to obtain the biomass of four typical forest types in Shangri-La, Yunnan Province, China. In addition, we adopted a geostatistical sampling method for sample point layout and optimization to achieve the purpose of improving sampling efficiency and accuracy, and compared with the traditional sampling method. The main results showed that (1) the Gaussian model, exponential model, and spherical model were used to analyze the variogram of the four typical forests biomass, among which the exponential model had the best fitting effect (R2 = 0.571, RSS = 0.019). The range of the exponential model was 8700 m, and the nugget coefficient (C0/(C0 + C)) was 11.67%, which showed that the exponential model could be used to analyze the variogram of forest biomass. (2) The coefficient of variation (CV) based on 323 biomass field plots was 0.706, and the CV based on SGCS was 0.366. In addition, the Overall Estimate Consistency (OEC) of the simulation result was 0.871, which can be used for comparative analysis of traditional and spatial sampling. (3) Based on the result of SGCS, with 95% reliability, the sample size of traditional equidistant sampling (ES) was 191, and the sampling accuracy was 95.16%. But, the spatial sampling method based on the variation scale needed 92 samples, and the sampling accuracy was 93.12%. On the premise of satisfying sampling accuracy, spatial sampling efficiency was better than traditional ES. (4) The accuracy of stratified sampling (SS) of four typical forest areas based on 191 samples was 97.46%. However, the sampling accuracy of the biomass variance stratified space based on the SGCS was 93.89%, and the sample size was 52. Under the premise of satisfying the sampling accuracy, the sampling efficiency was obviously better than the traditional SS. Therefore, we can obtain the conclusion that the spatial sampling method is superior to the traditional sampling method, as it can reduce sampling costs and solve the problem of sample redundancy in traditional sampling, improving the sampling efficiency and accuracy, which can be used for sampling estimation of forest biomass.

DSSIM-HR: A FORTRAN 90 program for direct sequential simulation with histogram reproduction

O objetivo deste trabalho foi avaliar o desempenho da simulação sequencial gaussiana (SSG) e da simulação sequencial indicatriz (SSI) na modelagem da incerteza das predições do K disponível em área de cana-de-açúcar, e comparar as simulações com o método já consagrado de krigagem ordinária (KO). Uma malha amostral com 626 pontos foi instalada em área de 200 ha, no Município de Tabapuã, em São Paulo. As simulações reproduziram a variabilidade dos dados amostrais de K disponível, enquanto a KO superestimou os baixos teores de K e subestimou os altos. O mapa de desvio-padrão obtido a partir da KO mostrou menor variação ao longo da área de estudo, quando comparado aos mapas obtidos a partir das simulações. A SSI obteve acurácia 22% superior à obtida pela SSG, na modelagem da função de distribuição condicional do K. As simulações apresentam maior eficiência que a KO para modelar incerteza na distribuição espacial do K. A SSI apresenta melhor desempenho que a SSG na estimativa dos teores de K disponível, em área de cana-de-açúcar.

The results of numerical simulation and comparison with experimental data of the aerodynamic characteristics of a blunt cone are presented. Two authors’ computer codes were used, intended for the numerical integration of the Navier-Stokes and Euler equations on tetrahedral unstructured and multi-block structured computational grids. Alternative numerical models on unstructured grids are analyzed in detail.

The representation of subgrid‐scale orography is a challenge in the physical parameterization of orographic gravity‐wave sources in weather forecasting. A significant hurdle is encoding as much physical information with as simple a representation as possible. Other issues include scale awareness, that is, the orographic representation has to change according to the grid cell size and usability on unstructured geodesic grids with non‐quadrilateral grid cells. This work introduces a novel spectral analysis method approximating a scale‐aware spectrum of subgrid‐scale orography on unstructured geodesic grids. The dimension of the physical orographic data is reduced by more than two orders of magnitude in its spectral representation. Simultaneously, the power of the approximated spectrum is close to the physical value. The method is based on well‐known least‐squares spectral analyses. However, it is robust to the choice of the free parameters, and tuning the algorithm is generally unnecessary. Numerical experiments involving an idealized setup show that this novel spectral analysis performs significantly better than a straightforward least‐squares spectral analysis in representing the physical energy of a spectrum. Studies involving real‐world topographic data are conducted, and reasonable error scores within ±10% error relative to the maximum physical quantity of interest are achieved across different grid sizes and background wind speeds. The deterministic behavior of the method is investigated along with its principal capabilities and potential biases, and it is shown that the error scores can be iteratively improved if an optimization target is known. Discussions on the method's limitations and broader applicability conclude this work.

A nested multi-grid solution algorithm has been developed for an adaptive Cartesian/Quad grid viscous flow solver. Body-fitted adaptive Quad (quadrilateral) grids are generated around solid bodies through ‘surface extrusion’. The Quad grids are then overlapped with an adaptive Cartesian grid. Quadtree data structures are employed to record both the Quad and Cartesian grids. The Cartesian grid is generated through recursive sub-division of a single root, whereas the Quad grids start from multiple roots—a forest of Quadtrees, representing the coarsest possible Quad grids. Cell-cutting is performed at the Cartesian/Quad grid interface to merge the Cartesian and Quad grids into a single unstructured grid with arbitrary cell topologies (i.e., arbitrary polygons). Because of the hierarchical nature of the data structure, many levels of coarse grids have already been built in. The coarsening of the unstructured grid is based on the Quadtree data structure through reverse tree traversal. Issues arising from grid coarsening are discussed and solutions are developed. The flow solver is based on a cell-centered finite volume discretization, Roe's flux splitting, a least-squares linear reconstruction, and a differentiable limiter developed by Venkatakrishnan in a modified form. A local time stepping scheme is used to handle very small cut cells produced in cell-cutting. Several cycling strategies, such as the saw-tooth, W- and V-cycles, have been studies. The V-cycle has been found to be the most efficient. In general, the multi-grid solution algorithm has been shown to greatly speed up convergence to steady state—by one to two orders. Copyright © 2000 John Wiley & Sons, Ltd.

We derive a new method of conditional Karhunen-Loève (KL) expansions for stochastic coefficients in models of flow and transport in the subsurface, and in particular for the heterogeneous random permeability field. Exact values of this field are never known, and thus one must evaluate uncertainty of solutions to the flow and transport models. This is typically done by constructing independent realizations of the permeability field followed by numerical simulations of flow and transport for each realization and assembling statistical estimates of moments of desired quantities of interest. We follow the well-known framework of KL expansions and derive a new method that incorporates known values of the permeability at given locations so that the realizations of the permeability field honor this data exactly. Our method relies on projections to an appropriate subspace of random weights applied to the eigenfunctions of the covariance operator. We use the permeability realizations constructed with our stochastic simulation method in simulations of flow and transport and compare the results to those obtained when realizations are constructed with sequential Gaussian simulation (SGS). We also compare efficiency and stochastic convergence with that of stochastic collocation.

Airborne hazardous plumes inadvertently released during nuclear/chemical/biological incidents are mostly of unknown composition and concentration until measurements are taken of post-accident ground concentrations from plume-ground deposition of constituents. Unfortunately, measurements often are days post-incident and rely on hazardous manned air-vehicle measurements. Before this happens, computational plume migration models are the only source of information on the plume characteristics, constituents, concentrations, directions of travel, ground deposition, etc. A mobile ''lighter than air'' (LTA) system is being developed at Oak Ridge National Laboratory that will be part of the first response in emergency conditions. These interactive and remote unmanned air vehicles will carry light-weight detectors and weather instrumentation to measure the conditions during and after plume release. This requires a cooperative computationally organized, GPS-controlled set of LTA's that self-coordinate around the objectives in an emergency situation in restricted time frames. A critical step before an optimum and cost-effective field sampling and monitoring program proceeds is the collection of data that provides statistically significant information, collected in a reliable and expeditious manner. Efficient aerial arrangements of the detectors taking the data (for active airborne release conditions) are necessary for plume identification, computational 3-dimensional reconstruction, and source distribution functions. This report describes the application of stochastic or geostatistical simulations to delineate the plume for guiding subsequent sampling and monitoring designs. A case study is presented of building digital plume images, based on existing ''hard'' experimental data and ''soft'' preliminary transport modeling results of Prairie Grass Trials Site. Markov Bayes Simulation, a coupled Bayesian/geostatistical methodology, quantitatively combines soft information regarding contaminant location with hard experimental results. Soft information is used to build an initial conceptual image of where contamination is likely to be. As experimental data are collected and analyzed, indicator kriging is used to update the initial conceptual image. The sequential Gaussian simulation is then practiced to make a comparison between the two simulations. Simulated annealing is served as a postprocessor to improve the result of Markov Bayes simulation or sequential Gaussian simulation.

Integrated modelling framework for enhancement history matching in fluvial channel sandstone reservoirs

The paper deals with the design of the material laying trajectory on the technological mandrel surface and the complex geometric shape mandrel surface model representation in automated systems for preparing control programs for winding composite materials products. The technological mandrel surface model can be represented as an irregular spatial point set. It is proposed to use an approach based on small surface segment approximation and modification of the differential equations system intended for integration laying material trajectories over an analytically given surface. The developed mathematical apparatus for constructing curves on surfaces given by irregular spatial point set makes it possible to construct smooth class-second curves without the need to first obtain the complete surface model. The proposed solutions adequacy are confirmed by the numerical experiments carried out on modeling the filament laying trajectory on various complex-profile mandrels given by an irregular point set and by the results of winding prepared control programs running out on a real multiaxis machine.KeywordsWindingMandrel surfacePoint cloudComposite material productCNC winding machineLaying material trajectory

To effectively design the vibrating flow pump (VFP) for left ventricular assist device, the numerical codes were developed for three-dimensional blood flow based on the finite volume method. The numerical codes were also developed based on the artificial compressibility method by the use of unstructured grid. Three-dimensional numerical computations and the visualizations were made for flow patterns in the casing of VFP, which were closely connected with hemolysis and blood coagulation. We examined the three different inlet conditions, i.e., radial flow, flow considering the 2nd vibration mode of the jellyfish valve motion, and the swirling flow, to explore the suitable condition for preventing the hemolysis and the blood coagulation. It was found that the swirling flow could effectively decrease hemolysis. The effect of rheology model of the blood flow was also studied in detail.