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I would like to know if I should switch to OPENFOAM for my task. I work only with Cartesian grids, right now in 2d, rectangular domains only. If $\mathbf{w} = (w_1, w_2)$ and suppose I want to solve

$\partial_t(\mathbf{w}) = \nabla(\mathrm{div} \mathbf{w}) = \mathbf{f}$

subject to Dirichlet boundary condition and an initial condition.

What I want to do is discretize in the following way and solve:

$\dfrac{w_1^{(n+1)} - w_1^n}{\tau} - \partial_{xx}w_1^{(n+1)} = f_1 + \partial_{xy}w_2^n \\ \dfrac{w_2^{(n+1)} - w_2^n}{\tau} - \partial_{yy}w_2^{(n+1)} = f_1 + \partial_{yx}w_1^{(n+1)}$.

  1. Need 2 tridiaogonal solves ( so Ax = b is trivial)
  2. I have made my choice of time stepping, and also the discretization.
  3. I might modify my time stepping and discretization later.
  4. Right now, I wrote a program myself in C

Basically I want to avoid doing the routine tasks like organize the MAC grid, store source values at the cell centre, compute $\partial_{xy}w_2^n$ given $w_2^n$ etc.

Q1) Is OPENFOAM overkill for my task and be more of a nuisance to actually implement the scheme I want to try ?

Q2) Am I better off doing what I am doing now, having a working code in C, which means though that each time I want to try something new, I have to change my program ?

Q3) Is it possible to use direct methods instead of iterative methods to solve my system in OPENFOAM ?

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  • $\begingroup$ I know it's totally outside of the scope of the question, but you might want to reconsider taking a Helmholtz decomposition approach to solving that system. Grad-div has a lot of nasty null space behaviours otherwise. $\endgroup$
    – origimbo
    Commented Mar 23, 2016 at 6:34
  • $\begingroup$ @origimbo: Thanks for the idea. How would that work? $w = \nabla \phi + u$ with $u$ having zero divergence ? I dont see how I will have enough information to solve for $\phi$ and $u$. $\endgroup$
    – me10240
    Commented Mar 23, 2016 at 6:46
  • $\begingroup$ Set $\mathbf{w} = \nabla \phi + \nabla \times \mathbf{A}$ where, since you're in 2D, you have a sensible gauge condition for $\mathbf{A}$ (i.e. non-zero in 3rd component only). You can solve for the initial conditions (and justify the evolution equations) by taking divergence and curl of $\mathbf{w}$ and inverting the resultant Laplacians. $\endgroup$
    – origimbo
    Commented Mar 23, 2016 at 7:06

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OpenFoam will definitely satisfy your needs. Though you may feel some restrictions of solvers,still it mostly resolves all the domains. Also Open Source platform has its advantage of large user-base and support by community. You can always give a try.

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  • $\begingroup$ by restrictions of solvers do you mean to say that no direct methods are available ? My system is tridiagonal so I dont want to use iterative methods for example. $\endgroup$
    – me10240
    Commented Mar 23, 2016 at 4:28
  • $\begingroup$ OpenFoam comes with interface tools that allow you to generate the mesh without going into the complexity and the hundreds lines of written code but at the same time understanding your needs you can manipulate. like for instance,i've been using IcoFoam solver for almost 2 months as i was working over incompressible laminar Navier-Stokes equations,and digging into it,there are many things that you can manipulate on later stage once you get to know how things work. I doubt without iteration if it's possible. If so,i'm surely looking forward to it. $\endgroup$ Commented Mar 23, 2016 at 4:54

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