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Engineering Stack Exchange

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.

45 questions
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2 answers

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 what I have thus far. The reaction taking place,…
Mierzen
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6
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2 answers

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 libraries such as cantera and thermopy as an…
Algo
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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 and you can make your comments on this specific…
ASK22
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4
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3 answers

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 given value, but the deflection may not be "small"…
Stilez
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4
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1 answer

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 following…
lahidj
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4
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1 answer

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 made a simple test to calculate $c_p$ of air at…
Algo
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3
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1 answer

Negative Eigenvalues in Ritz Solution of First-Order Shear Deformation Theory

I am trying to write a MATLAb code for determining the natural frequencies of a first-order shear deformation plate using Ritz method. I am using Legendre polynomials as trial functions in Ritz method, and my code works well for static analysis of…
Ali Baig
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2
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2 answers

Why does it take lesser iterations for a stiffer model in my FEA than a less stiffer model to converge?

I am currently using ANSYS FEA software and I conducted a simple geometric non-linear analysis of two same shaped bodies, but different cross sectional areas; one being quite bigger than the other. We know that the one with the bigger cross…
Rameez Ul Haq
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2
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2 answers

How to convert the velocity field to a pressure field for obtaining the sound level?

I am studying jet mixing noise and I am given a velocity field, with $V_x$, $V_y$, $V_z$ in the Cartesian coordinates. I wanted to know if there is a method by which I could find some information relating to the sound level produced from the…
fidafa123
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Finite difference discretization of the Cauchy-Riemann PDEs

I made a forward fd-discretization of the Cauchy-Riemann PDEs but I am struggling to implement this in python. I have a quadratic mesh with heighτ = $2*\pi$. The dirichlet boundary conditions are at $u(x,0) = f(x) = \cos(x)$ and $v(x,0) = g(x) =…
Rico227
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Convergence problem in RANS simulation of unsteady flow

I am simulating an air flow through a two dimensional rectangular channel. The channel splits into two channels, one of them is followed by a 90 degree bend downwards and leads into a cylindrical volume through which the air flows out of the…
Simon Henn
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2
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1 answer

How to use the Ritz method with the weak form to approximate solution of differential equation

I am having trouble understanding how to approximate the solution to this problem using the Ritz method and the weak form: $$\frac{d^2u}{dx^2} - u=0; \ \ x \in [0,1]$$ $$u(x=0)=0; \ \ \frac{du}{dx} \bigg|_{x=1} = 20$$ We multiply the strong form of…
The Bosco
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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 am unable to understand this, how does Abaqus…
Schneider
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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 the Darcy flux (function of $x$ and $t$) and…
Vincent Tang
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4 answers

J2 orbit propagation problem in MATLAB (solver instability)

The problem is that when I try to solve the following equations of J2 perturbed gravity: function xdot = Gravity( ~ , x ) Re = 6378.137; J2 = 1.08262668e-3; mu = 398600.4418; r = norm(x(1:3)); % xdot = [x(4:6) % …
AliRD
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