ivan-pi / deformable-lbm

Deformable lattice Boltzmann method for diffusion in 1D moving domains

deformable-lbm

Deformable lattice Boltzmann method for diffusion in 1D moving domains

This repository implements the method described in,

Van Der Sman, R. G. M. (2014). Moisture transport in swelling media modelled with a Lattice Boltzmann scheme having a deforming lattice. Journal of Food Engineering, 124, 54-63. https://doi.org/10.1016/j.jfoodeng.2013.09.033

deformable-lbm's Issues

Generalize C1 orthogonal collocation helpers

deformable-lbm/lib/oc_helpers.c

Line 6 in d17744d

void prepare_edge_matrix_and_rhs(

This function help solves the algebraic equations for time-dependent problems. A description can be found here: https://faculty.washington.edu/finlayso/ebook/pde/OC/OCFE.htm

We should keep this function specific to

• axisymmetric solutions with symmetry at the center-line
• fixed-length intervals

We should generalize this function to:

• arbitrary polynomial order; a little more effort now, but it will pay off
• general boundary conditions on the right side

We should adapt the function to capture general linear Robin boundary conditions:

$$ au + bu' = c $$

// Either a or b must be nonzero, else the problem is undefined!
assert(a != 0.0 || b != 0.0); 

if (b) {
   if (a) {
      // Robin
   } else {
      // Neumann
   }
} else {
   // Dirichlet
}

Open question remains how to deal with more general non-linear conditions of the form,

$$ a(t,x,u) + b(t,x)u' = c(t,x) $$

or even non-local ones,

$$ \int_\Omega u(x) d\Omega = p(x,u(x))|_{\Gamma} $$

I'm guessing in this case, the explicit ODE form is inappropriate anyways, and we need a solver that can deal with the more general DAE form $F(t,y,y') = 0$.