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Questions tagged [numerical-methods]

Questions concerning problems which cannot be exactly solved, or where the exact solution may be much more difficult to acquire than a solution by numerical methods.

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Constructing a proper Finite Difference Scheme for 3-dim function using data

$$f(x,y)$$ $f$ is unknown and I want to estimates its derivatives $$\frac{\partial f}{\partial y}, \frac{\partial f}{\partial x} \text{ and } \frac{\partial f}{\partial x^2}$$ from a data set. I have ...
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2answers
36 views

Example of real-life problem solved with numerical methods? [closed]

I hope this is a suitable question to ask here. Well, I'm taking Numerical Methods this semester (also called 'Numerical Analysis' in some places). The term-assignment is to find a real-life problem ...
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28 views

How to formulate a 3D version of the Navier-Stokes equations in 2D for numerical solution?

I'm considering a topology optimization problem where the design domain is a rotating annulus (in $\mathbb{R}^2$). One of the adjoint equations of the Navier-Stokes system whose solution is to be used ...
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33 views

Need help in understanding an equation in solidification modelling

I am not able to understand the 2nd equation. These equations are to model a simple solidification of an alloy system, the equations are set on a region which is semi-liquid ( mushy region ) , The ...
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238 views

How does Abaqus calculate reaction force?

I wrote a UEL for one element and compared to a reference UEL (FEM), where the results agreed satisfactorily, except the reaction force. The stress, strain, strain energy all were pretty accurate. I ...
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33 views

Discretise this transport equation

I am trying to discretise the PDE: $$\phi \frac{\partial c}{\partial t}+\frac{\partial j}{\partial x}=0$$ where $c$ is a function of $x$ and $t$, and $j=qc-D(q)\frac{\partial c}{\partial x}$, $q$ is ...
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1answer
144 views

How to derive deformation gradient or displacement gradient?

In one of my project, I need deformation gradient or displacement gradient for some elements in my model that made by ABAQUS software and I can't find it directly, any suggestion or help would be ...
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1answer
35 views

Mechanical Engineering- Modeling contact in Abaqus

I have simulated a 2D model in Abaqus which indicates 2 main part, first a sector that represent as wheel and, second a rectangular that represent rail. the wheel and rail are in contact and wheel ...
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Does excitation matter in a time-domain simulation/computation of a transfer function of an LTI system?

Let's say I am running a FDTD simulation of a wave-equation to determine a transfer function of an LTI system: \begin{equation} H(f) = \dfrac{Y(f)}{X(f)}\ \end{equation} where $Y(f)$ and $X(f)$ are ...
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0answers
22 views

Using a turbulence model in a numerical wake modeling technique

If I were to model the wake of a wind turbine using a certain numerical method should I, or should I not, take into consideration a turbulence model and couple it with the numerical method being ...
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32 views

Assistance on FEM heat transfer problem

I was trying to solve the below mentioned differential eqn. through Finite element methods, but i got stuck up by how to consider boundary conditions(involves convection and radiation) and how to make ...
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2answers
494 views

J2 orbit propagation problem in MATLAB (solver instability)

The problem is that when I try to solve the following equations of J2 perturbed gravity: ...
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0answers
839 views

How to calculate effective strain in plane stress?

What is the correct formula to calculate the effective strain under plane stress conditions? In plane stress it is assumed that the out of plane stresses are zero. The out of plane strains are not ...
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0answers
60 views

How to solve this equation for equilibrium height in square capillaries numerically?

The equation given below is for calculating the equilibrium height of the meniscus (in the center) in square capillaries. $d \sqrt{c} =2kG[k,\theta]$ where $d$ and $c$ are size of capillary and ...
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3answers
528 views

Deflection of thin plate with 1 free edge and deflection > thickness

I have an thin uniform rectangular steel plate supported on 3 sides and free on one, and supporting a uniform load. I'm trying to determine what thickness of plate I need to keep deflection below a ...
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2answers
1k views

Normalization and Non-Dimensionalization of a mass balance equation

I would like to ask what is the difference (if any) between normalization and non-dimensionalization. I will try to explain what I have done until now with an equation that I would like to work with ...
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0answers
53 views

Sliding mode surface derivative exact matrix format (ds/dx)

Is there any suggestion on sliding surface state derivative matrix (ds/dx) format? ...
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1answer
95 views

Sliding mode surface derivative using numerical method

In the article Controller Design using Bifurcation Map for Aircraft Spin Recovery, the sliding surface derivative is obtained using a numerical method. The steady space system is defined by the ...
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2answers
360 views

External diffusion: calculation of surface concentration

I am struggling a bit with an external diffusion problem. I am trying to calculate the concentration at the surface (as well as surface reaction rate) and would like some help or guidance. Here is ...
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0answers
39 views

Verify parameters variation in local sensitivity coefficients for microkinetic model

I’m performing a sensitivity analysis for a model of a set of elementary chemical reactions. I’m considering the variation in species concentration ($c_{k}$) with respect to the forward reaction rate ...
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1answer
272 views

Different calculations for values of thermodynamic properties

While deciding what tool (library) to use for a simulation of a hybrid gas turbine plant, I found that different libraries/tools of thermodynamic properties yield different values than the other. I ...
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2answers
351 views

How are thermodynamics properties of gases and liquids calculated numerically?

I was wondering how the values of thermodynamic properties as enthalpy, entropy, internal energy, specific heat, specific volumes ... etc, of gases and liquids are calculated using programming ...