How do you assess the quality and suitability of different meshing techniques for high-order CFD simulations?

Evaluating Mesh Techniques for High-Order CFD Simulations: 1. Mesh Orthogonality: Low skew and well-aligned elements enhance accuracy. 2. Isotropic Elements: Preferred for capturing flow details uniformly in all directions. 3. Mesh Grading: Essential for refining areas with high gradients (boundary layers, shock waves). 4. Discontinuous Galerkin (DG) Meshes: Balance between precision and computational efficiency.

Assessing Quality and Suitability of Meshing Techniques for High-Order CFD: 1. Element Shape & Size: Ensure minimal skewness and smooth transitions for accurate results. 2. Spectral Element Methods (SEM): Preferred for high accuracy with fewer elements. 3. Mesh Adaptivity: Crucial for resolving complex flow features by refining based on solution gradients.

Mathematical formulation of CFD involves equations in the form of partial differential form. Higher the order, lesser will be the numerical error. Convergence of CFD simulations with higher order schemes depends primarily on quality of mesh, proper boundary conditions and initialization conditions. Higher resolution of flow features demands usage of higher discretization schemes

Significance of higher order schemes comes into discussion when CFD simulations demands accurate predictions with proper capturing of physics. Convergence of solution with higher order schemes demands high quality of meshes. capturing of flow physics on the other hand will enforce maintaining desired Y+ values, Prism layers, Proper capture of flow region ..etc. These two requirements creates challenging environment for a simulations engineer

Meshing for high-order Computational Fluid Dynamics (CFD) schemes is challenging due to: Mesh Quality: Requires smoother, often curved meshes for accuracy. Generation Complexity: More complex and time-consuming to create and adapt. Computational Demand: Higher per-element cost, needing careful balance with accuracy. Geometry Representation: Difficult to accurately mesh intricate shapes. Stability and Error: Increased susceptibility to numerical instabilities and complex error control. Overall, while offering superior accuracy, high-order schemes demand sophisticated meshing approaches to fully leverage their benefits.

For high-order CFD meshes, quality is measured by: Shape and Defeature: Minimal element defeature and appropriate shapes. Smoothness: Continuous and smooth polynomial representation across the mesh. Boundary Fit: Accurate conformity to the physical domain's boundaries. Adaptivity: Proper element size and polynomial degree for capturing solution details. Stability: Ensuring numerical stability through suitable condition numbers. Error Monitoring: Using indicators to evaluate discretization and interpolation errors. Essentially, a high-quality mesh accurately captures geometry, maintains numerical stability, and adapts to solution details for effective CFD simulations.

Good quality meshes are important in achieving accurate simulation results and helps in avoiding flow divergence . Mesh sizing functions should be selected wisely to capture geometrical features properly. Maintaining an orthogonal quality of 0.7 will help in controlling residual divergence issues. Smoothness of mesh indicates gradual transition and low aspect ratio elements also helps in easy convergence

Generally - if exist - a test-validated case is selected first. Then a mesh independency test is applied by running several cases with different mesh techniques. After obtaining very similar results, residuals and std-deviation of flow gradients can be checked. After observing no significant differences between the results, the case with less number of mesh and high accuracy can be selected to decrease the cost of simulation.

Mesh quality assessment initially starts with visually inspecting the mesh. this will give and overall idea on how well you captured the domain. tools such as Orthogonal quality, skewness, smoothness etc will gives qualitative assessment on quality of mesh. Mesh sensitivity, Y+ values etc are the studies that can be done post meshing operations to make sure the physics is captured correctly