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10 votes
3 answers
996 views

Methods of solving non-linear advection-diffusion systems beyond Newton-Raphson?

I'm working on a project where I have two adv-diff coupled domains through their respective source terms (one domain adds mass, the other subtracts mass). For brevity, I'm modeling them in steady ...
cbcoutinho's user avatar
7 votes
3 answers
451 views

Strong coupling of a non-linear multiphysic problem: failure with Newton Raphson method

I am trying to solve a multiphysic problem using finite elements and a Newton Raphson solution scheme. I have two non-linear subsystems that are coupled bi-directionally. The first subsystem includes ...
Johann's user avatar
  • 71
5 votes
0 answers
101 views

Evolutionary dynamics in vascularised tumors, PDE-ODE coupled system

I have to solve the following PDE-ODE system $$ \displaystyle{\partial_{t} n = \bigl[a(s) - b(s)(y - h(s))^{2} - d\int_{\mathbb{R}} n \, dy \; + \; \beta \, \partial^2_{yy} n \;} \\\\ \...
AleManara's user avatar
5 votes
0 answers
197 views

Time-stepping for coupled nonlinear PDEs

What are good references for time-stepping of the coupled incompressible Navier-Stokes-heat equation (Boussinesq flow), $$ \begin{cases} \rho\left(\dot{\mathbf{u}} + \mathbf{u}\cdot\nabla \mathbf{u}\...
Nico Schlömer's user avatar
4 votes
1 answer
2k views

How could we solve coupled PDE with finite difference method and Newton-Raphson method?

I'm trying to solve coupled PDE by Crank-Nicolson (CN) and Newton-Raphson method with MATLAB. I have used CN method but not for coupled problem. Please if someone could help let me know to add more ...
Milad Rezaee's user avatar
3 votes
2 answers
413 views

Modelling question: example of a physical phenomenon with this jump condition at an interface?

in our finite element class we were talking about interface problems our teacher came up with the following, where $K_i$ are two given functions and $u_i$ is the restriction of the solution $u$ to $\...
FEGirl's user avatar
  • 405
3 votes
2 answers
438 views

Solving coupled PDEs numerically on a semi-infinite domain with no-flux boundary conditions

I have the following system of PDEs for which I have given parameters $\gamma, \tau$ and $\mu$, $$\begin{align} T_t = &\ \gamma\,(L +\tau F-T)\\ F_t = & -F_x-(F-LT)\\ L_t = &\ \mu L_{xx}+...
mk112358's user avatar
3 votes
2 answers
365 views

ode45 with matrix initial conditions

EDIT: We have a coupled system of 10 ode each. The coupling presents in the last equation. I thought about using a matrix 10 by 2 as initial conditions. I also followed a similar question with the ...
axel's user avatar
  • 81
2 votes
1 answer
131 views

How to couple the vibro-acoustic equations by Mortar method for non-matching meshes?

Assume we have two domains $\Omega_a$ a acoustic domain with boundary $\Gamma_a$ and $\Omega_s$ a domain of a solid body with boundary $\Gamma_s$. $\Omega_a$ and $\Omega_s$ have the common interface $\...
Pepe's user avatar
  • 459
2 votes
1 answer
239 views

Numerical methods for coupled stiff PDEs

I'm dealing with a set of nonlinear coupled PDEs that have the form: \begin{align} \frac {\partial y_1}{\partial t} &= y_2y_3 - y_1 \tag{1}\\ \frac {\partial y_2}{\partial t} &= y_1y_3 - y_2 \...
Mathews24's user avatar
  • 568
2 votes
1 answer
283 views

Coupling Boundary Condition of one PDE with source term of another PDE

We have a system of equations, wherein the BC of one PDE is coupled with the source term of another PDE. We have a regular 2D unit grid in x and y. There are two PDEs to be solved The first PDE (...
Dr Krishnakumar Gopalakrishnan's user avatar
2 votes
0 answers
81 views

Dynamic Successive Over/under Relaxation (SOR) with several variables

I am solving a partial differential algebraic equation (PDAE) system which has the following dependent variables: $f=f(X,T)$ and $g=g(T)$, along with a few others My current method for coupling is ...
james506's user avatar
2 votes
0 answers
215 views

Segregated solving of a tightly coupled system of PDEs

To compute the evolution of a free surface between two incompressible, immiscible liquids, two tightly coupled equations have to be solved, the volume fraction advection and the Navier-Stokes ...
akid's user avatar
  • 719
1 vote
1 answer
255 views

Coupled PDE: a confusion in boundary condition setup

I have a coupled PDE problem(Poisson-Schrondinger system), i.e. first I need to solve an eigenvalue problem (Schrodinger problem discretized by Galerkin method) $$Ax=\lambda x, ~~~A=A(u)$$ the ...
lorniper's user avatar
  • 593
1 vote
3 answers
2k views

Unexpected results of MATLAB's ode45

Whilst working with MATLAB recently I encountered something odd that I cannot explain. I was using the ode45 solver to solve a system of two coupled second order ODEs. I wasn't convinced about the ...
Glo's user avatar
  • 59
1 vote
1 answer
54 views

Verification of coupled system of equations for light propagation

I am trying to simulate the propagation of light in material using the non-linear schrödinger equation (NLSE): $$\partial_zE=\frac{i}{2k_0}\nabla^2_\perp E+\frac{ik_0n_2}{n_0}\vert E\vert^2E-0.5\beta^{...
arc_lupus's user avatar
  • 563
1 vote
2 answers
170 views

Improving calculation algorithm for coupled PDEs

I have the following two PDEs: $$\partial_zU=\nabla_r^2U+\varrho U$$ $$\partial_t\varrho=a\vert U\vert^4$$ with $a$ a constant and $$dt=dz\cdot\frac{n}{c}$$ with $n$ the refractive index of a ...
arc_lupus's user avatar
  • 563
1 vote
0 answers
66 views

Combining fluid flow solver based on lattice Boltzmann method with a mechanical deformation solver based on finite element method

I'm thinking to couple my fluid flow solver based on lattice Boltzmann method with a mechanical deformation solver based on finite element method to take account for solid deformation in my models. In ...
GGG's user avatar
  • 173
1 vote
0 answers
72 views

How to get a theoretical background in nonlinear, coupled FEM systems

I'm currently developing simulations for coupled, nonlinear, multi-region systems. Basically, I use the Finite Element Method (FEM) to model each physical quantity in each region. The obtained ...
Michael's user avatar
  • 1,463
1 vote
0 answers
66 views

Help about Fluid-Fluid coupling techniques

I need a little help and advice with a project I want to do: the idea is to "couple" (I don't know whether I can call it like this) a conservative Navier-Stokes Solver (Fractional-step, 2nd order FDM) ...
Kbzon's user avatar
  • 251
0 votes
1 answer
571 views

Implementing odespy for system of PDEs

After trying to use RK4 to solve the below system of equations, it appears the output had large and fast oscillations even with an adaptive time step I incorporated using the Cash-Karp method. I am ...
Mathews24's user avatar
  • 568
0 votes
0 answers
17 views

Thermo Hydraulic Mechanical modeling of energy wall slab in camsol multiphysics

I am currently working on a complex simulation project involving an energy wall slab, and I need assistance in accurately modeling and validating it using COMSOL Multiphysics. Here are the details of ...
Hizbullah's user avatar
0 votes
0 answers
47 views

Finite elements algorith for a fluid in a tube with an elastic obstacle (Fluid-Solid coupling)

I want to solve the model of a tube with an elastic obstacle, something like a simple model of an vessel with a valve. The fluid is given by an evolutionary incompressible Navier--Stokes equations, ...
yemino's user avatar
  • 515
0 votes
0 answers
44 views

Isolated solving of coupled system of PDE [duplicate]

I would like to solve 3 differential equations for 3 unknowns. So I wrote a MATLAB code, which solves (using the '\' operator) these equation using a linear system of equations (in which the 3 ...
Johann's user avatar
  • 71