Questions tagged [coupling]
The coupling tag has no usage guidance.
24
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Over-specification of conjugate heat transfer coupling conditions
I am trying to implement steady state conjugate heat transfer using a monolithically coupled scheme. In this simulation, the computational domain is divided into fluid and solid subdomains. Over time, ...
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2
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409
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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 $\...
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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):
$$\partial_zE=\frac{i}{2k_0}\nabla^2_\perp E+\frac{ik_0n_2}{n_0}\vert E\vert^2E-0.5\beta^{...
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How to couple the vibro-acoustic equations by Mortar method for non-matching meshes?
Assume we have two domains $\Omega_a$ a acoustic domain with boundary $\Gamma_a$ and $\Omega_s$ a domain of a solid body with boundary $\Gamma_s$.
$\Omega_a$ and $\Omega_s$ have the common interface $\...
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Finite elements algorith for a fluid in a tube with an elastic obstacle (Fluid-Solid coupling)
I want to solve the model of a tube with an elastic obstacle, something like a simple model of an vessel with a valve. The fluid is given by an evolutionary incompressible Navier--Stokes equations, ...
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99
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Evolutionary dynamics in vascularised tumors, PDE-ODE coupled system
I have to solve the following PDE-ODE system
$$ \displaystyle{\partial_{t} n = \bigl[a(s) - b(s)(y - h(s))^{2} - d\int_{\mathbb{R}} n \, dy \; + \; \beta \, \partial^2_{yy} n \;}
\\\\
\...
- 61
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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 ...
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66
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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 ...
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170
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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 ...
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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 ...
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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 ...
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1
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238
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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 \...
- 578
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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 (...
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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 ...
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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 ...
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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 $\mu$,
$$\begin{align}
T_t = &\ \gamma\,(L +\tau F-T)\\
F_t = & -F_x-(F-LT)\\
L_t = &\ \mu L_{xx}+...
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Unexpected results of MATLAB's ode45
Whilst working with MATLAB recently I encountered something odd that I cannot explain. I was using the ode45 solver to solve a system of two coupled second order ODEs. I wasn't convinced about the ...
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How could we solve coupled PDE with finite difference method and Newton-Raphson method?
I'm trying to solve coupled PDE by Crank-Nicolson (CN) and Newton-Raphson method with MATLAB. I have used CN method but not for coupled problem. Please if someone could help let me know to add more ...
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Isolated solving of coupled system of PDE [duplicate]
I would like to solve 3 differential equations for 3 unknowns. So I wrote a MATLAB code, which solves (using the '\' operator) these equation using a linear system of equations (in which the 3 ...
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Strong coupling of a non-linear multiphysic problem: failure with Newton Raphson method
I am trying to solve a multiphysic problem using finite elements and a Newton Raphson solution scheme. I have two non-linear subsystems that are coupled bi-directionally.
The first subsystem includes ...
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Help about Fluid-Fluid coupling techniques
I need a little help and advice with a project I want to do: the idea is to "couple" (I don't know whether I can call it like this) a conservative Navier-Stokes Solver (Fractional-step, 2nd order FDM) ...
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Coupled PDE: a confusion in boundary condition setup
I have a coupled PDE problem(Poisson-Schrondinger system), i.e.
first I need to solve an eigenvalue problem (Schrodinger problem discretized by Galerkin method)
$$Ax=\lambda x, ~~~A=A(u)$$
the ...
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211
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Segregated solving of a tightly coupled system of PDEs
To compute the evolution of a free surface between two incompressible, immiscible liquids, two tightly coupled equations have to be solved, the volume fraction advection and the Navier-Stokes ...
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Time-stepping for coupled nonlinear PDEs
What are good references for time-stepping of the coupled incompressible Navier-Stokes-heat equation (Boussinesq flow),
$$
\begin{cases}
\rho\left(\dot{\mathbf{u}} + \mathbf{u}\cdot\nabla \mathbf{u}\...
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