Academic literature on the topic 'LSFD-U Solver'

The thesis deals with the meshless methods based on generalized finite difference procedure operating on the mere distribution of points. The work per se focuses on maturing the meshless LSFD-U solver as a standard industrial tool for Aerospace CFD. One of the purported advantages of this class of methods as opposed to finite- volume methods is that they can considerably ease the need for generating grids. This aspect has been truly exploited in this thesis by projecting the meshless LSFD-U solver as a Cartesian grid methodology. The point distribution required by the LSFD-U solver is obtained from Cartesian grids. The Cartesian grid with its immense potential for process automation and the LSFD-U method with its ability to discretize the conservation equations on any arbitrary point distribution, form a natural pair for solving complex engineering problems in an automated process. The thesis presents a number of complex configurations of industrial relevance where the point distribution for the meshless solver are obtained from Cartesian grids in short turn-around times and without any human intervention. The grid convergence of the 3D inviscid solver is also established on a sequence of Cartesian point distributions. The automation capability is one of the key requirements for solving multi-body dynamics, moving body and optimization problems. The CFD process on such problems primarily involves repetitive grid generation. Any need for human intervention and expertise in the CFD process seriously hampers the overall performance and productivity. The meshless LSFD-U solver offers complete automation in the CFD process regardless of the complexity in the configurations. This aspect has been demonstrated in this thesis by predicting the store trajectory using quasi-steady simulations. In order to understand these results better, the work has also been extended to include the viscous effects in the trajectory prediction (although within a finite volume framework) and the sensitivities of the 6-DOF model integration. An automated CFD process to determine the optimal flap location has also been included in the demonstrations. Mesh adaptivity is one of the important areas of focus in a CFD work-flow for obtaining high resolution CFD solutions. Adopting such methodology for the meshless LSFD-U solver is attempted in this thesis work. A residual-based grid adaptive strategy in which an estimate of the local truncation error is used to define length scales for adequately resolving the flow in a given region is developed in the context of the LSFD-U solver. An attempt has been made to evolve an automated termination of the grid adaptation, which establishes the efficacy of the proposed adaptive strategy. For the flows with discontinuities, a hybrid strategy is employed in which the smooth flow regions are adapted using the R-parameter and the limiter operational regions are adapted using the divergence of velocity based indicator. A critical milestone for the success of the meshless methods is their ability to simulate turbulent flows by the way of solving RANS equations using highly anisotropic point distribution. The LSFD-U RANS solver makes use of a wall resolved hybrid Cartesian grid for the viscous turbulent flow computations. The Spalart-Allmaras turbulence model implementation within the meshless framework is discussed in detail. A combination of high aspect ratio grids (in a finite volume parlance) exhibiting grid folding, which is common in domains with wall slope discontinuity, results in loss in accuracy and robustness of the meshless solver. In order to handle such issues, we have proposed a point adaptive strategy which detects such regions with grid folding and improves the grid quality by introducing points along the rays exhibiting grid folding. The 2D LSFD-U RANS solver is validated for complex high lift cases. The work also includes some attempts towards achieving a successful 3D LSFD-U RANS solver.

This work deals with discretizing viscous fluxes in the context of unstructured data based finite volume and meshless solvers, two competing methodologies for simulating viscous flows past complex industrial geometries. The two important requirements of a viscous discretization procedure are consistency and positivity. While consistency is a fundamental requirement, positivity is linked to the robustness of the solution methodology. The following advancements are made through this work within the finite volume and meshless frameworks. Finite Volume Method: Several viscous discretization procedures available in the literature are reviewed for: 1. ability to handle general grid elements 2. efficiency, particularly for 3D computations 3. consistency 4. positivity as applied to a model equation 5. global error behavior as applied to a model equation. While some of the popular procedures result in inconsistent formulation, the consistent procedures are observed to be computationally expensive and also have problems associated with robustness. From a systematic global error study, we have observed that even a formally inconsistent scheme exhibits consistency in terms of global error i.e., the global error decreases with grid refinement. This observation is important and also encouraging from the view point of devising a suitable discretization scheme for viscous fluxes. This study suggests that, one can relax the consistency requirement in order to gain in terms of robustness and computational cost, two key ingredients for any industrial flow solver. Some of the procedures are analysed for positivity as applied to a Laplacian and it is found that the two requirements of a viscous discretization procedure, consistency(accuracy) and positivity are essentially conflicting. Based on the review, four representative schemes are selected and used in HIFUN-2D(High resolution Flow Solver on UNstructured Meshes), an unstructured data based cell center finite volume flow solver, to simulate standard laminar and turbulent flow test cases. From the analysis, we can advocate the use of Green Gauss theorem based diamond path procedure which can render high level of robustness to the flow solver for industrial computations. Meshless Method: An Upwind-Least Squares Finite Difference(LSFD-U) meshless solver is developed for simulating viscous flows. Different viscous discretization procedures are proposed and analysed for positivity and the procedure which is found to be more positive is employed. Obtaining suitable point distribution, particularly for viscous flow computations happens to be one of the important components for the success of the meshless solvers. In principle, the meshless solvers can operate on any point distribution obtained using structured, unstructured and Cartesian meshes. But, the Cartesian meshing happens to be the most natural candidate for obtaining the point distribution. Therefore, the performance of LSFD-U for simulating viscous flows using point distribution obtained from Cartesian like grids is evaluated. While we have successfully computed laminar viscous flows, there are difficulties in terms of solving turbulent flows. In this context, we have evolved a strategy to generate suitable point distribution for simulating turbulent flows using meshless solver. The strategy involves a hybrid Cartesian point distribution wherein the region of boundary layer is filled with high aspect ratio body-fitted structured mesh and the potential flow region with unit aspect ratio Cartesian mesh. The main advantage of our solver is in terms of handling the structured and Cartesian grid interface. The interface algorithm is considerably simplified compared to the hybrid Cartesian mesh based finite volume methodology by exploiting the advantage accrue out of the use of meshless solver. Cheap, simple and robust discretization procedures are evolved for both inviscid and viscous fluxes, exploiting the basic features exhibited by the hybrid point distribution. These procedures are also subjected to positivity analysis and a systematic global error study. It should be remarked that the viscous discretization procedure employed in structured grid block is positive and in fact, this feature imparts the required robustness to the solver for computing turbulent flows. We have demonstrated the capability of the meshless solver LSFDU to solve turbulent flow past complex aerodynamic configurations by solving flow past a multi element airfoil configuration. In our view, the success shown by this work in computing turbulent flows can be considered as a landmark development in the area of meshless solvers and has great potential in industrial applications.

This work deals with discretizing viscous fluxes in the context of unstructured data based finite volume and meshless solvers, two competing methodologies for simulating viscous flows past complex industrial geometries. The two important requirements of a viscous discretization procedure are consistency and positivity. While consistency is a fundamental requirement, positivity is linked to the robustness of the solution methodology. The following advancements are made through this work within the finite volume and meshless frameworks. Finite Volume Method: Several viscous discretization procedures available in the literature are reviewed for: 1. ability to handle general grid elements 2. efficiency, particularly for 3D computations 3. consistency 4. positivity as applied to a model equation 5. global error behavior as applied to a model equation. While some of the popular procedures result in inconsistent formulation, the consistent procedures are observed to be computationally expensive and also have problems associated with robustness. From a systematic global error study, we have observed that even a formally inconsistent scheme exhibits consistency in terms of global error i.e., the global error decreases with grid refinement. This observation is important and also encouraging from the view point of devising a suitable discretization scheme for viscous fluxes. This study suggests that, one can relax the consistency requirement in order to gain in terms of robustness and computational cost, two key ingredients for any industrial flow solver. Some of the procedures are analysed for positivity as applied to a Laplacian and it is found that the two requirements of a viscous discretization procedure, consistency(accuracy) and positivity are essentially conflicting. Based on the review, four representative schemes are selected and used in HIFUN-2D(High resolution Flow Solver on UNstructured Meshes), an unstructured data based cell center finite volume flow solver, to simulate standard laminar and turbulent flow test cases. From the analysis, we can advocate the use of Green Gauss theorem based diamond path procedure which can render high level of robustness to the flow solver for industrial computations. Meshless Method: An Upwind-Least Squares Finite Difference(LSFD-U) meshless solver is developed for simulating viscous flows. Different viscous discretization procedures are proposed and analysed for positivity and the procedure which is found to be more positive is employed. Obtaining suitable point distribution, particularly for viscous flow computations happens to be one of the important components for the success of the meshless solvers. In principle, the meshless solvers can operate on any point distribution obtained using structured, unstructured and Cartesian meshes. But, the Cartesian meshing happens to be the most natural candidate for obtaining the point distribution. Therefore, the performance of LSFD-U for simulating viscous flows using point distribution obtained from Cartesian like grids is evaluated. While we have successfully computed laminar viscous flows, there are difficulties in terms of solving turbulent flows. In this context, we have evolved a strategy to generate suitable point distribution for simulating turbulent flows using meshless solver. The strategy involves a hybrid Cartesian point distribution wherein the region of boundary layer is filled with high aspect ratio body-fitted structured mesh and the potential flow region with unit aspect ratio Cartesian mesh. The main advantage of our solver is in terms of handling the structured and Cartesian grid interface. The interface algorithm is considerably simplified compared to the hybrid Cartesian mesh based finite volume methodology by exploiting the advantage accrue out of the use of meshless solver. Cheap, simple and robust discretization procedures are evolved for both inviscid and viscous fluxes, exploiting the basic features exhibited by the hybrid point distribution. These procedures are also subjected to positivity analysis and a systematic global error study. It should be remarked that the viscous discretization procedure employed in structured grid block is positive and in fact, this feature imparts the required robustness to the solver for computing turbulent flows. We have demonstrated the capability of the meshless solver LSFDU to solve turbulent flow past complex aerodynamic configurations by solving flow past a multi element airfoil configuration. In our view, the success shown by this work in computing turbulent flows can be considered as a landmark development in the area of meshless solvers and has great potential in industrial applications.