Advanced Computational Models

Advanced Computational Models Grid Adaptation Non-conformal Interfaces Moving Boundaries Deforming Boundaries…

ME469B/4/GI

1

Grid Adaptivity

The computational grid can be refined and/or coarsened based on geometrical and numerical solution data

Useful for: Capture flow features in details Increase resolution in near-wall regions Improve grid quality …

ME469B/4/GI

2

Grid Adaptivity Example Computational Domain Flow in a complex passage

A uniform triangular grid is likely to be inappropriate to capture all the feature of the flow ME469B/4/GI

3

Adaptation Process

Definition of the adaptation function (based on geometrical and/or solution data) Selection of the cells to be refined or coarsened (marking or tagging) Selection of grid refinement/coarsening scheme Adaptation Interpolation of the previous solution onto the new grid (automatic)

ME469B/4/GI

4

Adaptation Functions

Geometrical Region Boundary Volume

Solution based Isovalue Gradient y+

ME469B/4/GI

5

Region Adaptation This is the same option we used for “global” grid refinement to study the grid convergence of the solutions Adapt Æ Region Select a region shape

Input the geometrical definition of the region ME469B/4/GI

6

Boundary Adaptation Adapt Æ Boundary Select a boundary of the computational domain

Three options: cell distance normal distance volume distance

ME469B/4/GI

7

Boundary Adaptation Adaptation based on a cell’s distance from the selected boundary measured in number of cells. (1 means only the cells attached to the boundary) Adaptation based on a cell’s normal distance from the selected boundary

Adaptation based on a target boundary volume (specify a target volume and a growth factor a)

Vcell = Vtarget e ad This adaptation attempts to generate boundary-layer type grid

ME469B/4/GI

8

Volume Adaptation Adapt Æ Volume Based on cell volume (area in 2D):

Two options: magnitude (threshold values) change (neighbor change)

ME469B/4/GI

Allow to compute the range in your grid

9

Isovalue Adaptation Adapt Æ IsoValue All field values are available (including equation residuals, customized and gridrelated functions)

Method: specify the function specify a range specify the inside/outside option ME469B/4/GI

10

Gradient Adaptation As before all field values are available (including equation residuals, customized and grid-related functions)

Adapt Æ Gradient

Method: specify the function specify a range Note that the option is refine/coarsen Cells above the Refine Threshold are Refined Cells below the Coarsen Threshold are Coarsened ME469B/4/GI

11

y+ Adaptation Useful for turbulent flow simulations

Adapt Æ y+

Method: specify the wall boundaries specify the range (as before)

Note y* is a friendlier version of y+ y+ = r yp ut /m ME469B/4/GI

y* = r Cm1/4 kp1/2 yp /m 12

Mark (Tag) and display Before performing the adaptation you can mark the cell selected (based on a certain adaptation function) and display them

Adapt Æ Region Æ Control Æ Display

Only the selected cells will be displayed

ME469B/4/GI

13

Mark or Adapt? Mark allows to evaluate the effect of a refining/coarsening procedure without actually changing the grid

Marked cells are saved in registers that can be combined or manipulated before Adapting

adapt

mark

Adapt is usually used only at the end when all The desired cells are marked

ME469B/4/GI

14

Managing Registers Marked cells are saved in registers

Adapt Æ <method> Æ Manage

Adapt registers: collection of cells Mask registers: binary tagging to all cells in active and inactive

Operations on the registers are: Union: combine two adapt registers (or more) Intersection: combine adapt and mask registers Change Type: convert a adapt in mask and viceversa Delete: eliminate a register Exchange: swap an adapt register (coarse Æ refine) Invert: swap a mask register (active Æ inactive) Limit: apply the adaptations limits to a register Fill: mark for coarsening all the cells not in the register ME469B/4/GI

15

Adaptation controls Set limits on the adaptation procedure (i.e. maximum number of final cells)

Adapt Æ <method> Æ Manage Æ Control

Select the adaptation scheme Conformal Hanging Nodes

ME469B/4/GI

16

Hanging-Node and Conformal Adaptation

Cell to be refined

ME469B/4/GI

17

Hanging-Node Adaptation

father

Selected cells (father) are refined homothetically (kids) Nodes are added on the edges of the father cell and connectivity information are generated to link the kids to the father neighbors

kids

Memory penalty associated to the additional connectivity Information required and to the presence of an inactive father cell Neighboring cells are not allowed to differ more than one-level of refinement (because of inaccuracy related to large volume variations) Coarsening can be only performed on previously refined regions. Kids are deleted and the father cell becomes active ME469B/4/GI

18

Conformal Adaptation Selected cells are refined by splitting the longest edge It is inherently conservative because the cell connectivity is not modified No memory penalty (the old cells are deleted and the only the new are stored) Low quality meshes can be improved (refinement not homothetic) Coarsening can be applied everywhere and corresponds to a local remeshing Can only be applied to triangular (tetrahedral) grids In is NOT as local as the hanging-node approach

ME469B/4/GI

19

Grid Adaptivity Guidelines

Surface mesh should be fine enough to capture all the essential geometrical features of the model (especially for high curvature surfaces) The initial mesh should be fine enough to capture the overall features of the flow A reasonably converged solution must be obtained before adapting the grid Suitable flow-adaptation criteria are crucial to obtain increased resolution of selected region (i.e. velocity gradients are better than pressure gradient in incompressible flows and high values of turbulent quantities are relevant for turbulent flows)

ME469B/4/GI

20

Boundary Grid Adaptivity Poor boundary resolution cannot be improved via grid refinement

Original geometry ME469B/4/GI

21

Non-conformal grids Grid generation can be simplified in certain problems by meshing various components separately. The grids have to be coupled using a non-conformal interface

Quadrilateral grid

Triangular grid ME469B/4/GI

22

Non-conformal grid interfaces The matching conditions between the two faces have to be defined Coupled interface: the interface is actually an internal face (no bc) Periodic interface: the matching allows to specify pressure gradients Define Æ Grid Interface

ME469B/4/GI

23

Non-conformal grid interfaces - Example Channel flow Periodic Boundaries

Non-conformal interface ME469B/4/GI

Velocity contours (cell values) 24

Non-conformal Interface Guidelines

Grid interface can be of any shape (2D and 3D) but the surfaces to be mached MUST be based on the same geometry especially for highly curved surfaces Grid resolution at the two sides of the interfaces can be different; accuracy (and fluxes conservation) degrades for highly different mesh size Non-conformal interfaces are binary connectivity between two (and only two) zones.

ME469B/4/GI

25

Moving Zones Several industrial applications involve flow through a domain which contains a moving component (propellers, turbines, etc.)

stationary

moving

Time ME469B/4/GI

26

Advanced Computational Models

• Grid Adaptivity • Non-Conformal Grid Interfaces • Moving Zones

ME469B/4/GI

27

Modeling Moving Zones

Different approaches can be followed: 1) 2) 3) 4) 5) 6)

Single Reference Frame Model (SRFM) Multiple Reference Frame Model (MRFM) Mixing Plane Model (MPM) Sliding Mesh Model (SMM) Mesh Deformation Remeshing

ME469B/4/GI

28

Single Reference Frame Model Simplest model available; entire computational domain is referred to a rotating reference frame (domain moves with the reference frame) The equations are rewritten in the moving reference frame and a Coriolis acceleration term appears as a source for the momentum balance Boundaries that move with the frame can assume any shape BUT boundaries that are stationary MUST be surface of revolution

ME469B/4/GI

29

Single Reference Frame Set-Up Define Æ Models Æ Solver Velocity formulation Absolute: the unknowns are the field variables in the stationary reference frame Relative: the unknowns are the field variables in the moving reference frame Note: the relative is only available in the Segregated solver and it is usually faster

ME469B/4/GI

30

Single Reference Frame Boundary Conditions Define Æ Boundary Condition Æ Fluid

Define the axis of rotation Select moving reference frame Define the angular speed

ME469B/4/GI

Æ Wall

Stationary surfaces: zero absolute rotational speed Moving surfaces: zero rotational speed relative to the adjacent zone 31

Multiple Reference Frame Model

Many rotating machinery problems involve stationary components that cannot be represented as surface of revolution or move at different velocity The extension is to consider separate reference frames for each component The set-up is similar to the SRFM MRFM ignores the relative motions of subdomains and the Coriolis body-forces are local to each region (no equivalence between stationary and moving reference frame) Suitable for problems where the interaction between rotating and non-rotating components is small ME469B/4/GI

32

Sliding Mesh Model Like the MRFM the domain is divided into moving and stationary components Unlike the MRFM the mesh in each subdomain moves with respect to one another and the problem is inherently unsteady The equations are solved in the stationary reference frame and the meshes are moved at each time step (no approximations to the governing equations) The sliding mesh interface is defined as a non-conformal interface

ME469B/4/GI

33

SMM Example

time

ME469B/4/GI

Velocity distribution

34