Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [coupling]

The tag has no usage guidance.

1
vote
0answers
34 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 ...
1
vote
2answers
152 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 ...
1
vote
0answers
62 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 ...
0
votes
1answer
313 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 ...
3
votes
1answer
183 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 \...
2
votes
1answer
171 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 (...
2
votes
0answers
57 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 ...
10
votes
3answers
608 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 ...
3
votes
2answers
205 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}+...
1
vote
3answers
1k 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 ...
4
votes
1answer
1k 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 ...
0
votes
0answers
40 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 ...
7
votes
3answers
357 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 ...
1
vote
0answers
61 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) ...
1
vote
1answer
211 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 ...
2
votes
0answers
159 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 ...
4
votes
0answers
180 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}\...