The comsol installation guide replaces the earlier comsol installation and operations guide and comsol quick installation guide with more focus on how to install the comsol software. Jul 01, 2016 i have two lat and lon matrices, each 622x810 and they are of a curvilinear projection. Div, grad and curl in orthogonal curvilinear coordinates. To compute how much heat energy has been transferred from radiator. The vertical contours are the coordinates for the electric field line and the horizontal contours are the coordinates for the tunneling boundary. Advanced fluid dynamics 2017 navier stokes equation in. Plotting data on curvilinear coord projection matlab. The comsol multiphysics software offers different methods for defining curvilinear coordinate systems. Orthogonal curvilinear coordinates particle in cell. A model of an anisotropic sshaped material was generated using the automated curvilinear coordinates feature in comsol multiphysics.
The solution for the coordinates was done, however, in the physical plane on a rectangular grid using interpolation at the curved boundaries, rather than in the transformed plane. Vector v is decomposed into its u, v and wcomponents. Divergence in orthogonal curvilinear coordinate system. A lot of materials have anisotropic properties and, in many cases, the anisotropy follows the shape of the material. Nov 26, 2015 in geometry, curvilinear coordinates are a coordinate system for euclidean space in which the coordinate lines may be curved.
Discussion closed this discussion was created more than 6 months ago and has been closed. The fundamental curve for constructing an appropriate coordinate system conforming the waveguide boundaries is defined by rho rho. Gradient, divergence and curl in curvilinear coordinates. Curvilinear coordinate system article about curvilinear. In comsol multiphysics, tools like named selections help maintain your model setup and streamline your workflow. Note that while comsol employees may participate in the discussion forum, comsol software users who are onsubscription should submit their questions via the support center for a more comprehensive response from the technical support team. Here we present a successful automated verification example of a local comsol 5. May 15, 20 the latest version of comsol multiphysics, version 4.
Topologically, the curvilinear grid is a cubic lattice with unit distance between grid points. The addon modules blend in seamlessly with comsol multiphysics, and the way you operate the software remains the same no matter which addon products are engaged. Cylindrical system, and spherical system can also be defined relative to a work. The latest version of comsol multiphysics, version 4. This means that one can convert a point given in a cartesian coordinate system to its curvilinear coordinates and. Adaptive method of curvilinear coordinates in comsol.
In this version, you can specify local coordinate systems for easier geometry. Cylindrical and spherical coordinates are just two examples of general orthogonal curvilinear coordinates. Hello, i want to visualize the stress tensor in the cylindrical coordinate. Any good book on vector or tensor analysis should provide you with a first principles derivation for some specific curvilinear coordinate systems spherical and cylindrical systems for example. Choose from 1d, 2d, and 3d geometries using cartesian coordinates and, for most application modes, 1d. These functions transform cartesian coordinates to channel fitted curvilinear coordinates with respect to a given curve. For cartesian coordinates the normalized basis vectors are e.
This is clearly visible in the curved sections of the solder joints, where the. This document provides a very nice treatment of coordinate transformation using the index notation. Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Oak ridge national laboratory, research reactors division, oak ridge, tn, usa. The comsol multiphysics geometry and cad environment 320. In order to define the cross sectional geometry of our uniform waveguides, we start by defining a curvilinear coordinate system. Other readers will always be interested in your opinion of the books youve read. Simulating the tunneling current across a graded heterojunction. Curvilinear coordinates are a coordinate system where the coordinate lines may be curved. Curvilinear coordinates utilize a coordinate system where the coordinate lines, or axes, can be curved.
Question about adaptive method for curvilinear coordinates. In geometry, curvilinear coordinates are a coordinate system for euclidean space in which the coordinate lines may be curved. How do i make a nonlinear solver converge in comsol multiphysics. I want to know the dimensions of the pipe and its position in the model exactly so that i can make some desired changes to the model. Wellknown examples of curvilinear coordinate systems in threedimensional euclidean space r 3 are cylindrical and spherical polar coordinates.
Curvilinear coordinate systems for curve geometric shapes make it easy to define anisotropic material properties in bent geometric shapes. Get the boundary mesh elements and generate a new combined boundary mesh. I previously just used vectors of lon and lat to plot my data with surfacem see below but i am not sure how to do this with lat and lon as a matrix of curvilinear coordinates. Curvilinear coordinate adaptive method in comsol physics forums. It would be convenient to have an idea about how does the ecoil vector. The cylindrical polar system is related to cartesian coordinates x. For example in lecture 15 we met spherical polar and cylindrical polar coordinates. Im trying to understand how the divergence formula in curvilinear coordinates is derived, but unfortunately my textbook doesnt go into much detail. Jan 22, 2016 these functions transform cartesian coordinates to channel fitted curvilinear coordinates with respect to a given curve. The solutions of two curvilinear coordinates interfaces. Comsol software users who are onsubscription should submit their questions via the support center for a more comprehensive response from the technical support team. For the more general case, you need to understand that your definition for the dot product of two vectors is valid only for cartesian coordinates. P q1,q2,q3,vx,vy,vz g 12 where the qs are the curvilinear position of a particle, and the vs are the cartesian components of the velocity. Simulation results reveal highly directed heat conduction.
We propose a method for solving the divcurl problem on a structured nonorthogonal curvilinear grid. Comsol desktop is a powerful integrated environment designed for crossdisciplinary product development with a unified workflow, regardless of the application area. In your past math and physics classes, you have encountered other coordinate systems such as cylindri. Applications velocity components acceleration components group problem solving applications the cylindrical coordinate system is used in. Is there a way to easily display the current cursor location co ordinates in the 3d graphics view in comsol 4. Guidelines for equationbased modeling in axisymmetric. Here, the curvilinear coordinates 12 3, are the familiar rz. Defining curvilinear coordinates for anisotropic materials.
An introduction to curvilinear orthogonal coordinates overview throughout the first few weeks of the semester, we have studied vector calculus using almost exclusively the familiar cartesian x,y,z coordinate system. Verifying that a local software installation performs as the developer intended is a potentially time consuming but necessary step for safety related. Apart from these predefined methods, the comsol software also provides a userdefined input, as usual. To find the curvilinear coordinate for three functions of f f 1 x, y, z, f 2 x, y, z, and f 3 x, y, z, set each function to a. To relate them to cartesian coordinates we usually assume that the zaxis is the polar axis. Divergence in orthogonal curvilinear coordinate system question. To solve three heat transfer problems with theoretical method and comsol model method 4. Two coordinate systems cylindrical polar coordinates. Engineers and scientists use the comsol multiphysics software to simulate designs, devices, and processes in all fields of engineering, manufacturing, and scientific research comsol multiphysics is a simulation platform that encompasses all of the steps in the modeling workflow from defining geometries, material properties, and the physics that describe specific phenomena to. Note that comsol multiphysics features a curvilinear coordinates interface that can be used to generate nonstandard coordinate systems.
Shown is the fluid velocity field and species concentration. Determine velocity and acceleration components using cylindrical coordinates. Orthogonal, curvilinear coordinates, author unknown. This section shows how to calculate these derivatives in other coordinate systems. The new user interface for automatic computation of curvilinear coordinates is a very practical addition to version 4. A mechanical simulation of a wrench computing the effective stress and deformation simulation of fluid flow and chemical transport in a micromixer.
Other way to look at it is by look at the coordinate lines. To simulate the heat transfer processes between room and a radiator by using comsol multiphysics software. To start a new discussion with a link back to this one, click here. We denote the curvilinear coordinates by u 1, u 2, u 3. This cylindrical system is itself a special case of curvilinear coordinates in that the base vectors are always orthogonal to each other. To provide a general introduction to comsol multiphysics software 3. Information about comsol commands and its general operation is now available in the comsol multiphysics reference manual. In this article we derive the vector operators such as gradient, divergence, laplacian, and curl for a general orthogonal curvilinear coordinate system. This curvilinear coordinates tool, included in comsol multiphysics, can be applied for any type of physics, like anisotropic thermal conductivity in heat transfer. Comsol multiphysics 5 same filename as the mphfile plus the extension. The name curvilinear coordinates, coined by the french mathematician lame, derives from the fact that the coordinate surfaces of the curvilinear systems are curved. Finding coordinates and dimensions of a point in comsol model. Such body shapes include spheres, ellipses, spherically capped cones, flatfaced cylinders with rounded corners, circular disks, and planetary probe vehicles.
You can learn more about how to use the curvilinear coordinates interface and how to solve anisotropic problems on curvilinear coordinate systems on the comsol blog. Comsol multiphysics automated installation verification via livelink for matlab m. The sides of the small parallelepiped are given by the components of dr in equation 5. Oct 11, 2015 surface and flux integrals, parametric surf. The differential operators are discretized using a macscheme for the unknowns in such a way that the discrete counterparts of the usual vector analysis relations are satisfied. Comsol multiphysics automated installation verification via. It uses splines to parameterize the curve to its arclength. These coordinates may be derived from a set of cartesian coordinates by using a transformation that is locally invertible a onetoone map at each point. Have you tried to add a second coordinate system in your model tree. These coordinates may be derived from a set of cartesian coordinates. Heres a look at three tutorial videos demonstrating how to create and utilize explicit, coordinate based, boolean, and adjacent selections. The particle is located by the radial distance r from a fixed point and by an angular measurement. Curvilinear coordinate adaptive method in comsol physics.
Divergence in curvilinear coordinates, continued first show that r e3 h1h2 0 problem 1 assume e 1 e 2 e 3 orthogonal coordinate system, and then obviously rx 1 e1 h1 and rx 2 e2 h2, and rx 1 rx 2 e3 h1h2, and next r e 3 h 1h 2 r rx 1 rx 2 the vector relations at the end of chapter 6 help to work out the righthand. To find the curvilinear coordinate for three functions of f f 1 x, y, z, f 2 x, y, z, and f 3 x, y, z, set each function to a constant u 1, u 2, and u 3, which defines each function as a. Orthogonal curvilinear coordinates for multiconnected regions, including. Currently, i have the output from a 3d solid mechanical model. Please login with a confirmed email address before reporting spam. However, on curvilinear systems those lines have non zero curvature justifying the name curvilinear coordinates. Oct 29, 2018 the solutions for the two curvilinear coordinates interfaces are shown in the figure below. Vector and tensor algebra in threedimensional curvilinear coordinates note. Curvilinear coordinates file exchange matlab central.
Please contact me if you have the link, or if you would like my copy of this document. According to description of the method, the adaptive method adapts the computed vector field to. I used the status bar display often to decide where to place slices for slice plots etc. Cartesian to curvilinear coordinate forward and backward. Comsol multiphysics software understand, predict, and. Comsol multiphysics quick start and quick reference. Automated installation verification of comsol via livelink.
Next we calculate basis vectors for a curvilinear coordinate systems using again cylindrical polar. I have a cylinder that changes the angle is constant the twodimensional space and i need the divergence in. Get the coordinates for each boundary mesh and determine the offset that we need for the boundary mesh elements to point to the correct coordinates. May 02, 20 hi all i have a little problem with coordinate transformation using the base vector coordinate system. Suppose now we take an infinitesimally small cube with edges parallel to the local curvilinear coordinate directions, and therefore with faces satisfying u i constant, i 1, 2, 3 for the three pairs of faces. Aug 03, 2010 is there a way to easily display the current cursor location coordinates in the 3d graphics view in comsol 4. A generalized curvilinear orthogonal coordinate system is presented which can be used for approximating various axisymmetric and twodimensional body shapes of interest to aerodynamicists. Blog defining curvilinear coordinates for anisotropic materials. An electrical simulation of a pacemaker electrode with computed voltage and current distribution the comsol desktop is a powerful integrated user. Orthogonal curvilinear coordinate systems suppose that the cartesian coordinates x,yz are expressed in terms of the new coordinates x12 3,xx by the equations x xx x x 12 3, yyxxx 12 3, zzxxx 12 3, where it is assumed that the correspondence is unique and that the inverse mapping exists. May 28, 20 curvilinear coordinates are a coordinate system where the coordinate lines may be curved. Comsol api for use with java through which the user can automate the process. Curvilinear coordinate systems for curve geometric shapes make it easy to define. This curvilinear coordinates tool, included in comsol multiphysics, can be applied for any type of physics, like anisotropic thermal conductivity in heat transfer, orthotropic materials for structural mechanics, and anisotropic media in electromagnetics, for example.
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