A new topography adapted mesh generation framework tailored to simulate Atmospheric Boundary Layer (ABL) flows on complex terrains is presented. The mesher is fully automatic given: the maximum and ...minimum surface mesh size, and the mesh size at the top of the ABL. The following contributions to the meshing workflow for ABL flow simulation are performed. First, we present a smooth topography modeling to query first and second-order geometry derivatives. Second, we propose a new adaptive meshing procedure to discretize the topography based on two different metrics. Third, we present the ABL mesher, featuring both prisms and tetrahedra. We extrude the triangles of the adapted surface mesh, generating prisms that reproduce the Surface Boundary Layer. Then, the rest of the domain is meshed with an unstructured tetrahedral mesh. In addition, we detail a hybrid quality optimization approach for both the surface and volume meshers, analyzing its impact on the solver for high-complexity terrains. We analyze the convergence of the triangle adaptive approach, obtaining quadratic convergence to the geometry and reducing to one-half the error for the same amount of degrees of freedom than without adaptivity and optimization. We also study the mesh convergence of our Reynolds-averaged Navier–Stokes (RANS) solver, obtaining quadratic mesh convergence to the solution, and using a 30% of the degrees of freedom while reducing a 20% of the error of standard semi-structured approaches. Finally, we present the generated meshes and the simulation results for a complete complex topographic scenario.
•Topography modeling to query first and second-order derivatives of the geometry.•Metric-driven mesh adaptation procedure for topographic scenarios.•Hybrid meshing framework for ABL flow simulation on complex topographies.•Hybrid optimization framework, detailing the impact on the RANS solver.•Analysis of the convergence to the topography geometry and to the solution.
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We detail how to use Newton’s method for distortion-based curved r-adaption to a discrete high-order metric field while matching a target geometry. Specifically, we combine two terms: a distortion ...measuring the deviation from the target metric; and a penalty term measuring the deviation from the target boundary. For this combination, we consider four ingredients. First, to represent the metric field, we detail a log-Euclidean high-order metric interpolation on a curved (straight-edged) mesh. Second, for this metric interpolation, we detail the first and second derivatives in physical coordinates. Third, to represent the domain boundaries, we propose an implicit representation for 2D and 3D NURBS models. Fourth, for this implicit representation, we obtain the first and second derivatives. The derivatives of the metric interpolation and the implicit representation allow minimizing the objective function with Newton’s method. For this second-order minimization, the resulting meshes simultaneously match the curved features of the target metric and boundary. Matching the metric and the geometry using second-order optimization is an unprecedented capability in curved (straight-edged) r-adaption. This capability will be critical in global and cavity-based curved (straight-edged) high-order mesh adaption.
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•Second-order optimization for simultaneous curved r-adaption to metric and geometry.•Objective function accounting for metric and geometry deviations.•Implicit model representation for 2D and 3D NURBS models.•First- and second-order derivatives of the implicit representation of the model.•First- and second-order derivatives of a log-Euclidean high-order metric interpolation.
•New automatic meshing framework for Atmospheric Boundary Layer (ABL) simulation on wind farms.•Conformal hybrid meshes of the ABL, topography and actuator discs, and with smooth size ...transitions.•New quality-based sweeping technique to generate hexahedral ABL conformal with the topography.•Mesh sizing characterization for different turbines in offshore and onshore cases.•Quadratic mesh convergence of the solver to the quantity of interest (flow across the turbine hub).
A new mesh generation process for wind farm modeling is presented together with a mesh convergence and sizing analysis for wind farm flow simulations. The generated meshes are tailored to simulate Atmospheric Boundary Layer (ABL) flows on complex terrains modeling the wind turbines as actuator discs. The wind farm mesher is fully automatic and, given the topography and the turbine characteristics (location, diameter and hub height), it generates a hybrid mesh conformal with the actuator discs and refined upwind and downstream. Moreover, it presents smooth element size transitions across scales and avoids extending high-resolution areas to all the domain. We take advantage of our automatic and robust mesher to study the mesh convergence of our RANS solver with linear elements, obtaining quadratic mesh convergence for a quantity of interest in all the tested cases. In addition, we quantify the mesh resolution at the terrain surface and at the actuator discs required to achieve a given numerical error in simulations in onshore and offshore frameworks. Finally, we present the generated meshes and the simulation results for an offshore and an onshore wind farm. We analyze in detail one particular wind direction for both cases, and for the onshore wind farm we use our automatic framework to estimate the yearly production of energy and measuring the error against the actual produced one.
We present a new incremental mesh morphing method obtained by proposing and discretizing a solution procedure for the continuous morphing problem. Our method seeks a diffeomorphism that transforms an ...initial domain to a final domain by only prescribing the boundary displacement. To this end, we propose to minimize the distortion of the morphing mapping constrained to satisfy the imposed boundary displacement. To solve this problem, we consider an augmented Lagrangian method in Hilbert spaces that incorporates the boundary condition in the objective function using the Lagrange multipliers and a penalty parameter. The distortion is devised to penalize the appearance of non-invertible mappings and therefore, we do not need to equip our discrete implementation with untangling capabilities. Moreover, we introduce a weight function to improve the quality of the deformation and thus, the robustness of the non-linear solver. The discretization of the continuous augmented Lagrangian method leads to a mesh morphing method suitable for large displacements and rotations of meshes with non-uniform sizing, and mesh curving of highly stretched high-order meshes.
•A new way to impose automatically incremental boundary conditions for mesh morphing.•Enhancing mesh quality with a weight function for the corresponding inner products.•Mesh morphing and mesh curving without the need of untangling capabilities.•The method is derived from a continuous domain morphing problem.•This work improves, in several aspects, our 26th IMR work.
We present a novel meshing and simulation approach for wind farms, featuring realignment and mesh adaptation. The turbines are modeled with actuator discs, which are discretized by means of an ...adaptation process to represent a level set function. The level-set-based simulation framework is combined with an adaptation cycle to capture both the solution and the actuator discs. In addition, we devise a turbine realignment process which takes into account the actual flow in the actuator disc configuration. Several results are presented to highlight the features of the approach. First, the adaptive simulation approach is validated, fulfilling the theoretical convergence rates and improving the accuracy of the boundary tight representations. Second, the adaptive simulation process is applied to a full wind farm configuration featuring 219 turbines, illustrating that is it well devised for complex wind farm configurations. Third, the turbine reorientation process is validated in a one turbine scenario. Finally, the realignment simulation framework is applied in a wind farm featuring 115 turbines. The presented results outline the significance of the proposed work, enabling turbine realignment and mesh adaptation to perform accurate simulations of complex wind farm configurations.
A method to optimize triangular and quadrilateral meshes on parameterized surfaces is proposed. The optimization procedure relocates the nodes on the surface to improve the quality (smooth) and ...ensures that the elements are not inverted (untangle). We detail how to express any measure for planar elements in terms of the parametric coordinates of the nodes. The extended measures can be used to check the quality and validity of a surface mesh. Then, we detail how to optimize any Jacobian-based distortion measure to obtain smoothed and untangled meshes with the nodes on the surface. We prove that this method is independent of the surface parameterization. Thus, it can optimize meshes on CAD surfaces defined by low-quality parameterizations. The examples show that the method can optimize meshes composed by a large number of inverted elements. Finally, the method can be extended to obtain high-order meshes with the nodes on the CAD surfaces.
We present a nodal interpolation method to approximate a subdivision model. The main application is to model and represent curved geometry without gaps and preserving the required simulation intent. ...Accordingly, we devise the technique to maintain the necessary sharp features and smooth the indicated ones. This sharp-to-smooth modeling capability handles unstructured configurations of the simulation points, curves, and surfaces. The surfaces correspond to initial linear triangulations that determine the sharp point and curve features. The method automatically suggests a subset of sharp features to smooth which the user modifies to obtain a limit model preserving the initial points. This model reconstructs the curvature by subdivision of the initial mesh, with no need of an underlying curved geometry model. Finally, given a polynomial degree and a nodal distribution, the method generates a piece-wise polynomial representation interpolating the limit model. We show numerical evidence that this approximation, naturally aligned to the subdivision features, converges to the model geometrically with the polynomial degree for nodal distributions with sub-optimal Lebesgue constant. We also apply the method to prescribe the curved boundary of a high-order volume mesh. We conclude that our sharp-to-smooth modeling capability leads to curved geometry representations with enhanced preservation of the simulation intent.
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•Interpolation of subdivision models with any degree and distribution.•Evidence of geometrical convergence rate for sub-optimal nodal distributions.•Featuring a unique all-in-one sharp-to-smooth modeling capability.•Automatically assisting the user to prescribe the simulation intent.•Readiness to prescribe the boundary of a high-order volume mesh.
We present an n-dimensional marked bisection method for unstructured conformal meshes. We devise the method for local refinement in adaptive n-dimensional applications. To this end, we propose a mesh ...marking pre-process and three marked bisection stages. The pre-process marks the initial mesh conformingly. Then, in the first n−1 bisections, the method accumulates in reverse order a list of new vertices. In the second stage, the n-th bisection, the method uses the reversed list to cast the bisected simplices as reflected simplices, a simplex type suitable for newest vertex bisection. In the final stage, beyond the n-th bisection, the method switches to newest vertex bisection. To allow this switch, after the second stage, we check that under uniform bisection the mesh simplices are conformal and reflected. These conditions are sufficient to use newest vertex bisection, a bisection scheme guaranteeing key advantages for local refinement. Finally, the results show that the proposed bisection is well-suited for local refinement of unstructured conformal meshes.
•A new multi-stage bisection for n-dimensional unstructured conformal meshes.•Suitable for local refinement.•Leads to conformal and reflected meshes after n uniform refinements.•In the third stage, the method favors conformity, finiteness, stability, and locality.
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