Machine Learning-Based Optimal Mesh Generation in Computational Fluid Dynamics

Abstract

Computational Fluid Dynamics (CFD) is a major sub-field of engineering. Corresponding flow simulations are typically characterized by heavy computational resource requirements. Often, very fine and complex meshes are required to resolve physical effects in an appropriate manner. Since all CFD algorithms scale at least linearly with the size of the underlying mesh discretization, finding an optimal mesh is key for computational efficiency. One methodology used to find optimal meshes is goal-oriented adaptive mesh refinement. However, this is typically computationally demanding and only available in a limited number of tools. Within this contribution, we adopt a machine learning approach to identify optimal mesh densities. We generate optimized meshes using classical methodologies and propose to train a convolutional network predicting optimal mesh densities given arbitrary geometries. The proposed concept is validated along 2d wind tunnel simulations with more than 60,000 simulations. Using a training set of 20,000 simulations we achieve accuracies of more than 98.7%. Corresponding predictions of optimal meshes can be used as input for any mesh generation and CFD tool. Thus without complex computations, any CFD engineer can start his predictions from a high quality mesh.

E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptation

“…These include the test function choice [7], forward solve [8], adjoint solve [9], derivative recovery procedure [10], error estimation [11], metric/monitor function/sizing field construction step [12,13,14], and the entire mesh adaptation loop [6,15,16].…”

“…The authors of [6] point out that, whilst goal-oriented mesh adaptation is a 'gold-standard' approach to mesh adaptation, it can be prohibitively computationally expensive and even infeasible to use, given that many solvers do not have automated adjoint capability. That work goes further than emulating the metric construction step of the mesh adaptation pipeline, covering the forward and adjoint PDE solve steps as well, so that the user of a trained network does not need to solve adjoint problems at all.…”

“…Similarly, [21] and [22] use neural networks to guide mesh gen-eration. From the user perspective, [6] also describes a mesh generator, albeit one that emulates a goal-oriented mesh adaptation loop.…”

“…ν = 0.5 ∈ [0.1, 1], b = 40 ∈ [10, 100] and u inflow = 5 ∈ [0. 5,6]. In order to test the approach more thoroughly, we consider some additional test cases whose problem specifications have key differences from the training cases.…”

A Review of Intelligent Airfoil Aerodynamic Optimization Methods Based on Data-Driven Advanced Models

“…In recent years, aerodynamicists have integrated data-driven methods with artificial intelligence techniques, thus contributing to the rapid development of the "fourth paradigm" in current aerodynamic research [20]. In the process of airfoil aerodynamic optimization, datadriven advanced models have been widely employed, including rapid prediction of flow field [21][22][23][24][25][26][27][28][29][30], super-resolution reconstruction [31][32][33][34][35][36][37][38][39][40][41], differential equation solution [42][43][44][45][46][47][48][49], and grid generation based on artificial intelligence model [50][51][52][53][54][55]. Sufficient data acquisition and advanced model construction are highly essential in the optimal design, having a significant impact on the accuracy and efficiency of airfoil aerodynamic optimization.…”