Unstructured Grid Flow Solver Research Articles

The evaporation and condensation model with interface tracking

Interface tracking simulation (ITS) is one of the promising approaches to describe heat transfer of boiling phenomena and their underlying mechanisms. Better understanding and modeling of this process will benefit various engineering systems relying on two-phase heat transfer. The presented research implements, verifies and validates the modeling capability of the evaporation process using a massively parallel unstructured grid flow solver, PHASTA. The verification of the evaporation and condensation model has been performed by comparing the bubble growth rate with analytical solutions. Both pool boiling and flow boiling simulations are performed using this ITS evaporation and condensation model. The bubble nucleation frequency in pool boiling simulation is validated against experimentally-based correlations. The bubble evolution and growth rate are compared with experimental data to validate the model performance under flow boiling condition. The authors propose an innovative ITS based-boiling model which can conduct boiling simulation with 3D unstructured computational mesh. This capability will serve as one of the most important building blocks for high resolution boiling simulation in realistic engineering geometries being developed under the PHASTA simulation framework. Compared to the structured-grid-based solvers, which are challenging to apply to complex engineering geometries, this boiling model implementation is capable of conducting high-resolution boiling simulations in engineering geometries and resolving the detailed hydrodynamics and thermal information for quantities of interest at/around the interface. This approach may help fulfill the numerical data gap between the local physical phenomena and the engineering scale ITS applications in the future.

Development of Fast Unstructured-Grid Flow Solver FaSTAR

Development of Fast Unstructured-Grid Flow Solver FaSTAR

Postlimiters and Simple Dirty-Cell Detection for Three-Dimensional Unstructured (Unlimited) Aerodynamic Simulations

The postlimiter (simple a posteriori slope limiter) is an anti-slope-limiting mechanism to preserve nominal second order in space as much as possible. This technique has been demonstrated to increase resolutions of two-dimensional simulations up to four times in each dimension [Kitamura, K., and Hashimoto, A., “Simple a posteriori Slope Limiter (Post Limiter) for High Resolution and Efficient Flow Computations,” Journal of Computational Physics, Vol. 341, July 2017, pp. 313–340]. This paper extends the postlimiter to three dimensions with an emphasis on ”dirty” (meaning ill-shaped) cells, which arise in practical three-dimensional (3-D) unstructured grids over complex geometries. Gradient accuracy is known to significantly deteriorate on dirty cells, and a slope limiter needs to be applied. However, the original postlimiter does not recognize dirty cells and deactivates a slope limiter. To address this issue, a simple dirty-cell detection method is proposed and incorporated into the postlimiter. The 3-D version of postlimiter (referred to as “postlimiter 3”) is successfully incorporated into fast aerodynamic routine (FaSTAR), a 3-D unstructured grid flow solver is developed at the Japan Aerospace Exploration Agency. Postlimiter 3 can handle general 3-D unstructured grids. Numerical examples support its efficiency, accuracy, robustness, and applicability to a wide spectrum of aerodynamic problems of high engineering importance.

Stabilized Finite Elements in FUN3D

A streamlined upwind Petrov–Galerkin (SUPG)–stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared with the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.

高速な非構造格子流体ソルバFaSTARの開発

高速な非構造格子流体ソルバFaSTARの開発

Application of the FUN3D Solver to the 4th AIAA Drag Prediction Workshop

FUN3D Navier–Stokes solutions were computed for the 4th AIAA Drag Prediction Workshop grid-convergence study, downwash study, and Reynolds-number study on a set of node-based mixed-element grids. All of the baseline tetrahedral grids were generated with the VGRID (developmental) advancing-layer and advancing-front grid-generation software package following the gridding guidelines developed for the workshop. With maximum grid sizes exceeding 100 million nodes, the grid-convergence study was particularly challenging for the node-based unstructured grid generators and flow solvers. At the time of the workshop, the super-fine grid with 105 million nodes and 600 million tetrahedral elements was the largest grid known to have been generated using VGRID. FUN3D Version 11.0 has a completely new pre- and postprocessing paradigm that has been incorporated directly into the solver and functions entirely in a parallel, distributed-memory environment. This feature allowed for practical preprocessing and solution times on the largest unstructured-grid size requested for the workshop. For the constant-lift grid-convergence case, the convergence of total drag is approximately second-order on the finest three grids. The variation in total drag between the finest two grids is only two counts. At the finest grid levels, only small variations in wing and tail pressure distributions are seen with grid refinement. Similarly, a small wing side-of-body separation also shows little variation at the finest grid levels. Overall, the FUN3D results compare well with the structured-grid code CFL3D. For the grid-convergence case, the FUN3D total and component forces/moments are within one standard deviation of the workshop core solution medians and are very close to the median values especially at the finest grid levels. The FUN3D downwash study and Reynolds-number study results also compare well with the range of results shown in the workshop presentations.

An Efficient Correction Method to Obtain a Formally Third-Order Accurate Flow Solver for Node-Centered Unstructured Grids

A new method of obtaining third-order accuracy on unstructured grid flow solvers is presented. The method involves a simple correction to a traditional linear Galerkin scheme on tetrahedra and can be conveniently added to existing second-order accurate node-centered flow solvers. The correction involves gradients of the flux computed with a quadratic least squares approximation. However, once the gradients are computed, no second derivative information or high-order quadrature is necessary to achieve third-order accuracy. The scheme is analyzed both analytically using truncation error, and numerically using solution error for an exact solution to the Euler equations. Two demonstration cases for steady, inviscid flow reveal increased accuracy and excellent shock capturing with no loss in steady-state convergence rate. Computational timing results are presented which show the additional expense from the correction is modest compared to the increase in accuracy.

PARALLEL UNSTRUCTURED-GRID FINITE-VOLUME METHOD FOR TURBULENT NONPREMIXED FLAMES USING THE FLAMELET MODEL

A parallel unstructured-grid finite-volume method has been developed to accurately and effectively handle physically and geometrically complex turbulent reacting flows. The parallel algorithm has been implemented to improve the computational efficiency of the unstructured-grid flow solver. The strong density-pressure-velocity coupling at all speeds is handled by the multiple pressure-correction method. In dealing with the turbulent nonpremixed flame fields, the turbulence-chemistry interaction is represented by the laminar flamelet model, which could be the optimum choice between accuracy and economy. Numerical results indicate that the present approach reasonably well predicts the overall features of the three-dimensional turbulent nonpremixed flame. However, there exist noticeable deviations between prediction and measurement. Based on numerical results of turbulent reacting flows, detailed discussions is given about the prediction capabilities and limitations or defects of the present numerical and physical models.

Tetrahedral finite-volume solutions to the Navier-Stokes equations on complex configurations

A review of the algorithmic features and capabilities of the unstructured-grid flow solver USM3Dns is presented. This code, along with the tetrahedral grid generator, VGRIDns, is being extensively used throughout the USA for solving the Euler and Navier–Stokes equations on complex aerodynamic problems. Spatial discretization is accomplished by a tetrahedral cell-centered finite-volume formulation using Roe's upwind flux difference splitting. The fluxes are limited by either a Superbee or MinMod limiter. Solution reconstruction within the tetrahedral cells is accomplished with a simple, but novel, multidimensional analytical formula. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart–Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the near-wall region of the boundary layer. The issues of accuracy and robustness of USM3Dns Navier–Stokes capabilities are addressed for a flat-plate boundary layer, and a full F-16 aircraft with external stores at transonic speed.

PARALLEL IMPLEMENTATION FOR SOLVING THE TWO-DIMENSIONAL NAVIER-STOKES EQUATIONS ON A CELL-CENTERED, UNSTRUCTURED GRID

A compressible, two-dimensional, unstructured-grid Navier-Stokes solver has been developed for subsonic viscous flows. Pseudo-time preconditioning is applied to improve low Much number convergence for primitive as well as conserved variables. The scheme was implemented on a workstation and on the Ncube2s, which utilizes the multiple-instruction, multiple-data (MIMD) approach to parallel computing. A detailed description of the implementation procedure for an unstructured-grid flow solver on a MIMD computer is given. Test cases include steady as well as unsteady flows.

Perspective on unstructured grid flow solvers

This survey paper assesses the status of compressible Euler and Navier-Stokes solvers on unstructured grids. Different spatial and temporal discretization options for steady and unsteady flows are discussed. The integration of these components into an overall framework to solve practical problems is addressed. Issues such as grid adaptation, higher order methods, hybrid discretizations and parallel computing are briefly discussed. Finally, some outstanding issues and future research directions are presented.

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Improved algorithms for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach, which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure

Accuracy of an unstructured-grid upwind-Euler algorithm for the ONERA M6 wing

Improved algorithms for the solution of the three-dimensional, time-dependent Euler equations are presented for aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured-grid flow solvers. The spatial discretization involves a flux-split approach that is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves either an explicit time-integration scheme using a multistage Runge-Kutta procedure or an implicit time-integration scheme using a Gauss-Seidel relaxation procedure, which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady flow results are presented for both the NACA 0012 airfoil and the Office National d'Etudes et de Recherches Aerospatiales M6 wing to demonstrate applications of the new Euler solvers. The paper presents a description of the Euler solvers along with results and comparisons that assess the capability.