Tutorial Created in Comsol 4.3 (2012)

1 R. White, Comsol Acoustics Introduction, 2012 Tutorial Created in Comsol (2012) R. White, Comsol Acoustics Introduction, 2012 Finite Element Analysis (FEA / FEM) Numerical Solution of Partial Differential equations (PDEs). representing the physics. on which to solve the problem. conditions (for static or steady state problems) and initial conditions (for transient problems). W - domain - boundary (or dW) Unknowns u(x,y,z) x y The Mathematical Problem: Independent Variables space and time (x,y,z,t) Dependent Variables unknown field (such as u) R. White, Comsol Acoustics Introduction, 2012 Finite Element Analysis (FEA / FEM) Boundary Conditions.

2 On each boundary you must specify either: 1)The dependent variable itself ( u) Essential Boundary Condition or Dirichlet Boundary Condition 2)The derivative of the variable itself ( du/dn) Natural Boundary Condition or Neumann Boundary Condition 3)The relationship between the dependent variable and its normal derivative ( du/dn=(1/z) u)). W - domain - boundary (or dW) Unknowns u(x,y,z,t) x y The Mathematical Problem: Independent Variables space and time (x,y,z,t) Dependent Variables unknown field (such as u) R. White, Comsol Acoustics Introduction, 2012 Finite Element Analysis (FEA / FEM) 1)Discretization of the space into pieces (the elements) this is called the Mesh.

3 2)Choice of element type - shape (triangle, quadrilateral, etc.), number of nodes (3, 4, 5, 8, etc.) and shape function (linear, quadratic, etc.). 3)Choice of solver (direct, iterative, preconditioning). 4)Post-processing looking at the solution in various ways. The Finite Element Part: The shape is now meshed with triangle elements. R. White, Comsol Acoustics Introduction, 2012 So, this is always the sequence for any FEA problem: on the representative physics (choose the PDE). the geometry on which to solve the problem. the material properties .. that is, all the constants that appear in the PDE. the boundary conditions (for static or steady state problems) and initial conditions (for transient problems).

4 An element type and mesh the geometry. a solver and solve for the unknowns. the results to find the information you want. R. White, Comsol Acoustics Introduction, 2012 Finite Element Packages - Here are some of the common ones R. White, Comsol Acoustics Introduction, 2012 Comsol Multiphysics - More recent than Ansys, Nastran, Abaqus. - Integrates well with Matlab (uses Matlab syntax too). - Focuses on Multiphysics coupling different physics together ( acoustics and solid mechanics). - Highly allows you to program in your own differential equations if they are not already implemented. R. White, Comsol Acoustics Introduction, 2012 1. Decide on the representative physics (choose the PDE).

5 Comsol Here we go!! I will focus on acoustics as an application, but the steps are similar for other physics. Choose how many dimensions to work in. Warning: 3D is usually a large computational problem, avoid if at all possible!! Make use of symmetries to get to 2D or 2D axisymmetric. Choose your type of physics. You may select more than one if you want coupling. Tutorial Created in Comsol (2012) Pressure Acoustics is what we have been doing in ME139 this solves the helmholtz equation for the complex acoustic pressure. Here you are choosing what kinds of solutions you want at the end of the study. You can always add other kinds later. R. White, Comsol Acoustics Introduction, 2012 Frequency Domain : This is what we have been doing for the most part in ME139.

6 The helmholtz equation .. you are solving for steady state pressure at a single frequency. Eigenfrequency : This will allow you to find the acoustic modes of a domain. These are frequencies and corresponding pressure fields where the helmholtz equation and boundary conditions can be satisfied with no external drive (Homogeneous Solutions) 1. Decide on the representative physics (choose the PDE) : Choose Type of Study . R. White, Comsol Acoustics Introduction, 2012 1. Decide on the representative physics (choose the PDE). Complete. At this point I have chosen my PDE and number of spatial dimensions. For pressure acoustics, my PDE is the Hemholtz equation.

7 But I can allow r0 and c to vary in space if desired. Remember, since I have chosen Pressure Acoustics , I have selected time-harmonic time-harmonic means single we are assuming time dependence ejwt. The pressure I solve for will be the complex pressure, 220ppcw 200110ppcwrr Constant density ( , , )pxyzSolved for in Comsol 10( , , , )Re( , , )1( , , )( , , )2( , , )( , , )20 logjtrmsrmsrefpxyztpxyzepxyzpxyzpxyzSPLx yzpw Can be easily computed in post processing using post processing tools inside Comsol . R. White, Comsol Acoustics Introduction, 2012 Comsol Graphical User Interface Model tree shows all parts of the model.

8 Geometry, boundary conditions, materials, types of study to run, results. Right click on things to interact. Geometry and various results plots will be shown in the main Graphics window. Various useful tools, depending on what you have selected in the model tree. Tools related to zooming, viewing, saving graphics objects. R. White, Comsol Acoustics Introduction, 2012 2. Define the geometry on which to solve the problem. Draw the geometry of the acoustic domain (the domain over which you want to solve the PDE) by right clicking on geometry and using various tools (tools also appear in the toolbar at the top when geometry is selected in the model tree).

9 If you select some objects in the graphics window then Boolean tools (like subtract, intersect, union) will also appear under geometry. Default units are mks units (SI units). You can change units by selecting the (root) object in the model tree (the very very top object). If you change or delete geometry objects, sometimes you may need to ask Comsol to Build All the geometry again to get it to refresh. For complicated geometry you may choose to import it from a CAD program. R. White, Comsol Acoustics Introduction, 2012 2. Define the geometry on which to solve the problem. Objects appear in here. Here are all the geometry objects I defined. Edit them by clicking and/or right clicking them in the model tree.

10 Drawing tools. For axisymmetric, the axis of symmetry will be r=0 and be drawn as a line in the graphics window. R. White, Comsol Acoustics Introduction, 2012 3. Set the material properties .. that is, all the constants that appear in the PDE. For pressure acoustics, all that matters is r0 and c. (And although that is set under Study | Frequency Domain , not under materials.) Under materials select open material browser or + material . Find the material you want in the browser, or create your own material with + Material . After you find it, right click and Add Material to Model For pressure acoustics, the only properties that matter are density and speed of sound.