Questions tagged [numerical-modelling]
The numerical-modelling tag has no usage guidance.
215
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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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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,...
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1
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88
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Improved euler on hybrid methods where both time and space are discretized?
I am trying to understand how to use the improved euler method on MPM simulations.
In the kind of MPM simulation I am doing with forward euler the order of operations is as follows:
Write particle ...
- 263
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Refluxing step on Finite difference AMR
Hi I am a computer scientist working on MHD code for astrophysics simulation. We use a finite difference scheme where we first solve the spatial derivatives and with them solve the right hand side and ...
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118
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How do the navier stoke equations model materials who "forget" their original form?
Sorry for the screenshot but I don't want to try to format this on latex:
We have this annotation of the Navier-Stokes equations:
I am particularly puzzled by the viscosity/stress term. For an ...
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Which analogs of Newton's multivariate method are faster?
Currently, I am studying a 2D nonlinear Schroedinger equation and searching for the fastest method.
$$
\begin{equation}
i \frac{\partial \psi}{\partial t} = [-\frac{1}{2} \nabla^2 + V_0(r) - i\gamma ...
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92
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A staggered grid for an eigenvalue problem (linear stability analysis)
I'm interested in extending the concept of a staggered grid (commonly used to solve the incompressible Navier-Stokes equations) to a linear stability analysis context. For example, we can consider ...
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Numerical code to solve LLG is not preserving norm
I am new to this thread. I am trying to do a simple exercise on solving the LLG equation. The equation reads:
$\frac{d\vec{m}}{dt} = -\gamma(\vec{m} \times\vec{H})$.
Given a normalized input state ($...
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Conceptual doubt regarding 2D conjugate heat transfer modelling (COMSOL and Mathemtica)
I have been dealing with some conceptual flaws in my understanding of modelling, which I will elaborate herein. I am modelling conjugate heat transfer of a reciprocating fluid, which flows with ...
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Fortran - Lid-Driven Cavity Boundary Conditions Error when using SIMPLE method
I am studying Numerical Methods for incompressible flows. part of the tasks is to model the lid driven cavity problem in 2D using the SIMPLE method.
I have been provided with Fortran code that is ...
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Compact Finite Differences for the Heat Equation with Robin Boundary Conditions
I am trying to solve the Heat equation with Robin Boundary condition:
$$ u_t(x,t) = u_{xx}(x,t), \\ u(x,0) = g(x), \\ u(0,t) + u_x(0,t) = h_0(t), \\ u(1,t) + u_x(1,t) = h_1(t)$$
for $ 0\leq x\leq1$ ...
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ValueError: array must not contain infs or NaNs; When using solve_ivp in the scipy library
I am solving an initial value problem using solve_ivp. The problem consists of computing the concentration profile of a set of reactions over time, given the initial concentrations and some of the ...
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Numerical Method for Multivariate Inversion Formula
For my research, I need to evaluate the density of a random vector $\boldsymbol{X} \in \mathbb{R}^p$ using the multivariate inversion formula. Let the density function of $\boldsymbol{X}$ be $f (\...
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Can numerical calculations be accepted as proof/refutation of a mathematical axiom?
In many cases, an algorithm can be designed and implemented to prove/disprove a mathematical axiom, but could it be accepted as proof or refutation by rigorous mathematicians?
user44517
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Faster convergence for minimizing least squares of forward modelling problems
This specific question was raised from optimizing parameters of column experiments in the hydrogeological context. I want to optimize a parameter of interest (in this case $D$), based on experimental ...
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Linear PDE solution with constraints
Consider the following linear PDE:
$$\nabla_q V(q) - M_d(q)M^{-1}(q)\nabla_q V_d(q) = 0,$$
where $V(q)$ and $M(q)$ are known and $M_d(q)$ is a grey box function (e.x., $M_d(q)$ is fitted using a ...
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Energy conservation in RK4 integration scheme in C++
My colleague and I are trying to study the three-body problem, with different integration schemes, starting from the two-body problem. We implemented the symplectic Euler scheme and the Runge–Kutta ...
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Using backward and forward Euler method to solve a certain stiff ODE
When using the backward and forward Euler methods to solve a certain stiff differential equation, what criteria does one look at before drawing the conclusion that one is more stable than the other?
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337
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How to extract intermediate calculation results from an SciPy ODE function in python?
I have a bit lengthier ODE function which was simulated by using Scipy solve_ivp function. During this simulation I calculated many parameters but as the output, I am taking out put only some other ...
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RK4 integration of the three-bodies problem with C++
first of all thank you for all the answers you gave me yesterday for the integration via Symplectic Euler's method of the three-body problem.
We managed to implement both Euler's and Runge Kutta 4's ...
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Boundary conditions for compressible Euler equations
I want to solve the compressible 1D Euler equations numerically.
Theory says that for subsonic inflows, one can prescribe two variables, e.g. pressure and temperature. Density can then be computed ...
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I'm working on a problem to proof the two-grid cycle, with ν1 pre-smoothing and ν2 post-smoothing steps
I'm facing trouble while proving the given formula. Could you please help me with this? Thanks :)
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Can I use MOL to solve 2D steady state PDE in terms of r and z spatial coordinates?
recently I need to solve a 2D steady state PDE equation.
It’s not time dependent, and the only two independent variables are z and r direction.
So far for this solution, I was thinking using Method ...
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1
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scipy.optimize.root not converging and RuntimeWarning
I am trying to solve the following problem:
$$ \frac{d^2y}{dx^2}=\sinh(y) $$
Where the boundary conditions are: $y(0)=-1$, and $ \frac{dy(x\rightarrow \infty)}{dx}=0 $. Through central difference ...
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2
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275
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Automatic differentiation of a numerical solver
We often want to use numerical methods to evolve a system in time.
That is, for a set of differential equations, we can specify some parameters $\bar{\theta}$ and pass these into our numerical solver ...
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Modelling a spring interpolation
I have parameters $T$ for tension, $b$ for bounciness and $P_t$ for target value that should be approached as t goes to infinity.
Currently I have written an equation like so:
$\ddot{f}(t)=\frac{T(P_t-...
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Looking for non-trivial examples of solutions to 3D wave equations?
We have developed a (new) numerical scheme to solve the classical wave equation in 3 dimensions and we aim to publish the results.
We can read in the aim and scope of the journal of computational and ...
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How do you handle the singularity in polar or cylindrical coordinates?
Governing equations in polar or cylindrical coordinates often have terms with $\frac{1}{r}$ involved. At $r = 0$, such terms blow up to become a "singularity." The Cartesian version of such ...
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A direct numerical method for determining a relaxation function from a known creep function
Both the creep function and the relaxation function are connected by the convolution integral. The usual method for calculating the relaxation function from a creep function or vice versa is to ...
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Solving detailed combustion kinetics in CFD, where to start?
I have some experience solving single- and multicomponent Euler equations for modeling of gas flows, including combustible ones. The code (variations of finite-difference WENO methods) is written with ...
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What are good particle dynamics ODEs for an introductory scientific computing course?
I'm teaching an introductory course on scientific computing (programming in C/C++) and am looking for application problems which the assignments can be centered around. I'm thinking of ODEs for ...
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How does non-dimensionalization improve the behavior of ODE solvers?
I have a set of coupled ODEs that I'm solving numerically. The independent variable is time and runs from values of $10^{15}$ to $10^{17}$ in units of seconds. The state variables in their usual ...
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Solving PDE with a non-linear constraint in MATLAB
I am trying to solve a DAE with a non-linear constraint. The governing equations have the following form.
The second equation is a constraint and it must be satisfied everywhere. Is there a way to ...
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137
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Is the Alternating-Directions Implicit method dependent on the space increment?
I am writing an Alternating-Directions Implicit Method for simple 2D diffusion ( \begin{equation*}
\frac{df(x,y,t)}{dt}=D\Delta u
\end{equation*}). Tridiagonal matrices are solved via Thomas ...
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Can someone explain why RK4 is less accurate for very small timesteps?
I am currently working on a project where I have used an RK4 integrator to attempt to solve the three-body problem. An interesting result that I found, was that decreasing the size of the time steps ...
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Recursion relations for integrating Gaussian functions
I'm trying to implement a numerical method used in quantum chemistry from scratch. I'm using this paper as a reference. It's also available on Sci-Hub. So, the method requires calculating integrals of ...
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Accurately solving system of differential equations
So I am trying to solve two equations simultaneously. The goal is to find values for $\frac{de}{dt}$ and $\frac{d}{dt}$ which are the rates of change of the variables $a$ and $e$. I am then ...
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Generalized Eigenvalue Problem using MATLAB
I'm trying to solve a generalized eigenvalue problem. I have two matrices $H$ and $S$ such that:
$$
HX=λSX
$$
I need to find the eigenvalues $\lambda$. The matrices $H$ and $S$ are real, asymmetric, ...
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What does the Chebyshev differentiation matrix look like for third and fourth derivative?
I have a PDE that contains both the 3rd derivative and 4th derivative. Example shown below
$$ \frac{\partial u}{\partial t} =\frac{\partial}{\partial x}(u^3\frac{\partial^3u}{\partial x^3}) $$
$$ \...
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Numerical diagonalization of Hamiltonian
Framework
I am trying to diagonalize the Bogoliubov-de Gennes Hamiltonian. The problem is that the Hamiltonian contains a Laplacian. This could be solved by using a discretized Laplacian.
How I tried ...
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Nondimensionalization of a multi-component chemical diffusion equation
Edit I've modified the equations because they were wrong and I added the whole system, as asked by @Wolfgang
I am trying to nondimensionalize a system of partial differential equations similar to 2nd ...
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Change in Variables applied to biharmonic equation
Background
I want to solve the following biharmonic equation:
$$\frac{ \partial^4 s }{ {\partial \xi}^4 }+\frac{ \partial^4 s }{ {\partial \xi}^2{\partial t}^2 }+\frac{ \partial^4 s }{ {\partial t}^4 }...
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Can I use periodic boundary conditions for `U` but not for `p`?
Cross-posted from Stack Overflow. (https://stackoverflow.com/questions/70686368/can-i-use-periodic-boundary-conditions-for-u-but-not-for-p)
I am trying to numerically compute the drag force around a ...
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How to model the dynamic impact of transport on boxes containing vials?
Let's consider that we have large number of boxes being transported in a truck. These boxes contain certain number of vials which in turn contain some other products. Now one would like to simulate ...
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Solving ODE with Spectral Method using Chebyshev Polynomials
I would like to solve following the basic equation of linear elasticity (for simplicity in 1D)
$$
\frac{d}{dx} \left( E \frac{du}{dx} \right) = 0 \quad \textrm{with} \quad u(1)=0, \; u(-1)=b
$$
...
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Is a 2021 MacBook Air sufficient for modeling and simulations research in fluid dynamics?
I code mostly in Matlab, simulating various simple fluid dynamics models.
One particular simulation has the potential to become sort of complex, though I believe the set of coupled equations will ...
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Mineral dissolution and solute transport around a solid
I am trying to simulate solute transport of acid (HCl) and consequent mineral dissolution around a grain (calcite).
The governing equation for transport is the advection-diffusion equation, given as:
...
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Solving and Plotting Mutualism Model in Python
I am a beginner in programming. I need to program a mutualism model of two species in python that would solve and graph using the following equations:
$$
\frac{dN_1}{dt} = N_1(r_1 - e_1N_1 + \alpha _{...
