Questions tagged [numerical-modelling]
The numerical-modelling tag has no usage guidance.
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Solve beam equation with elastic term using scipy solve_bvp
I want to solve the beam equation with distributed load and elatic term (which depends on how much the beam interact with the terrain) :
$$
EI\frac{d^4w}{dx^4}+k*(w(x)-t(x))=q(x)
$$
where $q(x)$ is a ...
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How can I apply a mixed boundary condition to a multi-material heat transfer problem using Crank-Nicolson?
I am working on a mixed material model for a melting material and need to enforce both a Dirichlet and Neumann type condition at the interface. Subject to an external surface heat flux at the top of ...
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Educational Purpose: How to synchronize chaotic systems
The graph plots the X coordinate of the synchronized Lorenz chaotic system. I am self learning by reading research articles on how to synchronize identical chaotic systems. But as seen from the figure,...
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Roadmap for Career Transition to Computational Science
What sort of path should I follow to make a the transition from high school physics to computational science?
Context
15 years teaching experience in physics and general science. Maths is currently ...
- 105
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Best finite difference scheme in 2D for the mixed derivative
The are good methods to deduce finite difference schemes for derivatives of functions of one variable. But how to get a good one for the mixed derivative of a function of two variables $u=u(x,y)$, ...
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shooting method to compute the interface shape
I am trying to use a shooting method to compute the shape of liquid-gas interface given by the following differential equation:
$$
\frac{d^2 \theta}{ds^2} = \frac{f(\theta)}{h(h + 3\lambda)}
$$
with $\...
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Preventing accumulation of state errors in surrogate models?
For surrogate models which predict derivatives based on the current state: how do you avoid the accumulation of state errors due to modeling error in each state update?
It seems to me that if you used ...
- 149
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MIP - Large Piecewise Linear Constraints Over Continuous Intervals
I'm currently trying to run a MIP (have access to both Gurobi and CBC) with a piecewise linear function having ~200 intervals for each of the ~30 x values I have. I am using the standard decomposition ...
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Discretization of 2D advection equation with non-constant speed
Suppose I have a 2D advection equation $$\frac{\partial \rho}{\partial t}=-\nabla\cdot(\vec{w}\rho)$$ with $\vec{w}=(u,v)$ non-constant and having zero divergence. I want to numerically solve this ...
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Does anyone know how to add a forcing term at the center of a cicular membrane?
I am here once again searching for wisdom, as some of you might notice I asked a related question a few days ago. And now I am struggling to add a forcing term at the center of the membrane, in order ...
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How is entropy taken into account in a FV solver?
When solving for a given PDE, how is the entropy taken into account? Does the fluxes has another form? Or is the entropy PDE for a given entropy-flux included in the solver?
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In electromagnetic simulation, how much does the feed model impact an antenna's directivity performance and E-field phase readings?
Question: How much would a simplified feed model in an EM simulation alter an antenna's directivity and the E-field phase reading when compared to using a more complicated/realistic feed model?
I am ...
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146
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Solving system of ODEs, where time derivative approaches infinity due top initial condition
I am trying to solve a problem in python using scipy's solve_ivp. The system of ODEs I am trying to solve is for coupled where I am solving for two time-dependent ...
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What is the difference between approximations of mixed derivative and how to implement it
currently I am solving 2D nonlinear second order differential equation containing mixed derivative. I started searching how to descretisize it and found two formulas for 4th order approximation. First ...
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Shallow water model for year-round watershed runoff
I have an (maybe not so clever) idea to apply the shallow water model for computing the year-round watershed runoff of a catchment. It means using of real topography with variable slopes and roughness,...
