Workshop

Workshop Download & Excute “Diamond_win32.msi”(Windows XP,Windows Vista 32bit, Windows 7 32bit users) Download & Excute “Diamond_x64.msi (Windows Vista 64bit, Windows 7 64bit users)

Workshop

Workshop

DIAMOND/PDE – 1D Problem Test  Heat conduction problem in a pipe R 1, T 1 R 2, T 2 1. Differential Equation 2. Exact solution 3. Numerical application T 1 = 70°CT 2 = 70°C R 1 = 18mmR 2 = 18mm Let’s consider a pipe with inner boundar y held at T 1 = 70°C for R 1 = 18mm and outer boundary at temperature T 2 = 20° C for R 2 = 20mm. Let’s determine the temperature distribution in the pipe. Let’s determine the temperature distribution in the pipe.

Workshop DIAMOND/PDE – 1D Problem  Heat conduction problem in a pipe 1. Geometry Define the Global interval for x : a < x < b and the number of segments 2. Select the method for the node generation (number of nodes and interval of each segment) 3. Accept

Workshop DIAMOND/PDE – 1D Problem  Heat conduction problem in a pipe 1. Geometry Global interval : 18 < x < 20 Number of segments : 1 Uniform Mesh Segment number : 1 Ratio : 1 Interval of Segment #1: 18 < x < 20 Number of nodes (NNODE): Global interval 1.2 Method of node generation

Workshop DIAMOND/PDE – 1D Problem  Heat conduction problem in a pipe 2. Element & Property Select the method for the element generation (number of elements for each segment) 2. Accept 3. Define the properties for each segment 4. Accept 2

Workshop DIAMOND/PDE – 1D Problem  Heat conduction problem in a pipe 2. Element & Property 2.1 Element Generation 2.2 Property definition Total Number of segments : 1 Elements (NELEM): 1< N < 200 Order of shape function (KIND): 1 Integration points : 1 NNODE-1=NELEM x KIND Total Number of properties : 1 Elements (NELEM): 1< N < 200 k(x) = xb(x)=0 c(x) = 0f(x)=0

Workshop DIAMOND/PDE – 1D Problem  Heat conduction problem in a pipe 3. Boundary conditions & 4. Loads Define the Boundary Conditions 2. Accept 3. Define internal Loads 4. Accept 2

Workshop DIAMOND/PDE – 1D Problem  Heat conduction problem in a pipe 3. Boundary conditions α 1 = 0 β 1 = 1γ 1 = 70 α 2 = 0 β 2 = 1γ 2 = 20 α 1 = 0 β 1 = 1γ 1 = 70 α 2 = 0 β 2 = 1γ 2 = 20 Dirichlet Boundary Conditions α 1 u’(x 1 ) + β 1 u(x 1 ) = γ 1 α 2 u’(x 2 ) + β 2 u(x 2 ) = γ 2 4. Load No load at a nodal point for our problem

Workshop DIAMOND/PDE – 1D Problem  Heat conduction problem in a pipe Input the exact solution 2. Input its derivative 3. Accept 2 5. Exact solution (optional)

Workshop DIAMOND/PDE – 1D Problem  Heat conduction problem in a pipe 5. Exact solution (optional) To calculate the error norm between the exact solution & the FEM solution To calculate the error norm between the exact solution & the FEM solution

Workshop DIAMOND/PDE – 1D Problem  Heat conduction problem in a pipe 6. Export an input file & 7. Run IPSAP 1 1. Generate an input file *.in 2. Run IPSAP (Process) 3. Plot the results 23

Workshop DIAMOND/PDE – 1D Problem  Heat conduction problem in a pipe Solution X and Y axis range 2. Error Norm L2 Error Norm = 1.56e-05

Workshop DIAMOND/PDE – 1D Problem Test 1. Properties 2. Exact solution & BC 3. Mesh generation 1)241 nodes, 1 st order shape function 2)241 nodes, optimization (3 segments)  Example Problem

Workshop DIAMOND/PDE – 1D Problem  Example problem 1. Geometry 1. Define the Global interval for x : 0 < x < 1 and the total number of segments 3 2. Then for each segment the method of node generation should be defined: Select the appropriate segment number Generate the local range Choose the number of nodes Accept 1 2

Workshop DIAMOND/PDE – 1D Problem 2. Element & Property 1. Select the total element segments, and then for each segment: Select the segment number Choose the starting and ending elements Choose the order of the shape function Choose the number of integration points Accept 2. Define the properties 1 2  Example problem