# Info on method of lines approach

 Register Blogs Members List Search Today's Posts Mark Forums Read August 9, 2007, 05:19 Info on method of lines approach #1 charlie ryan Guest   Posts: n/a Hi Im not sure if this is the right place to post this so excuse me! I have a system of 3 non linear first order pde's, differentiated with respect to time and one spatial dimension. I am thinking of using a method of lines approach for removing the spatial differentiation, and then using a runge - kutta technique [or something similar], to solve the left over coupled ode's. But i don't understand how the difference formulas, that you have from the finite difference method, can be solved numerically using a RK method. Take an example -> u_t = u_x. Using a central difference formula, u_x looks like; u_x = (u_i+1,j - u_i-1,j)/2h => u_t = (u_i+1,j - u_i-1,j)/2h Now how do i solve the above using a method from numerically solving ode's [RK method, Euler, whatever]? I'm confused about what to do when the i+1, i-1 is there - what do i do with these? Can anyone suggest a good reference on the method of lines? Any comments are appreciated! Charlie  August 9, 2007, 09:35 Re: Info on method of lines approach #2 opaque Guest   Posts: n/a Dear Charlie, Let me repose your example, using Dirichlet (value specified) conditions u_t = u_x u(t, x_a) = u_a u(t, x_b) = u_b u(t_0, x) = u_0 The method of lines can be applied to any of the dimensions of the problems, either t or x.. Let us go with "x" again. You discretize your interval (a,b) into a finite number of nodes separated by h, and then apply the difference formulas at each node, then u_i_t = (u_i+1,j - u_i-1,j)/2h for i = 1, 2, .. N for i = 1 u = u_a i = N u = u_b You got N-2 ODE's that are coupled. You can use a RK integrator. If you ODE's are linear you can find their analytical solution in closed form. Hope this helps, Opaque  August 9, 2007, 11:06 Re: Info on method of lines approach #3 charlie ryan Guest   Posts: n/a Thanks Opaque very helpful - it makes sense. I have a system of PDE's that look something like; h_t = -hv_x - h_x T_t = (T/h - Tv/h - E)h_x - Tv_x - vT_x - hE_x v_t = -vv_x - p_x +TE/h + v_xx + (1/h)v_x*h_x p_x = h_x + hxx + E^2 + T^2 E = f(x,h,E,v,t) I hope that is readable! So it is basically a system of PDE's (note only three involve time derivatives]. E is a function that depends on the rest of the variables, and p does not directly depend upon t. i have a set of inital conditions for the above. Now i understand how you solve one pde to get a system of ode's, but what about a system of coupled pde's looking something like above? How do you solve the pde's system, when you have multiple variables? Any help is very much appreciated, Charlie Thread Tools Search this Thread Show Printable Version Email this Page Search this Thread: Advanced Search Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are Off Pingbacks are On Refbacks are On Forum Rules Similar Threads Thread Thread Starter Forum Replies Last Post C-H Kuo Main CFD Forum 4 September 19, 2022 14:06 panda60 OpenFOAM Running, Solving & CFD 15 April 25, 2013 01:34 [Gmsh] discretizer - gmshToFoam Andyjoe OpenFOAM Meshing & Mesh Conversion 13 March 14, 2012 04:35 Anorky FLUENT 0 April 27, 2010 10:55 m-fry Main CFD Forum 1 April 20, 2010 14:40

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