# 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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### Casting and the pressure of the metal

Background A gold casting process is explained here: The casting metal is melted in a special casting machine that is programmed to insert the metal under vacuum into the flask at the right time, ...
13 views

### Accuracy of stable (not backward stable) numerical algorithm

I understand the definition of accuracy for a backward stable numerical algorithm, which shows how such a quantity depends both on machine-epsilon and on the condition number of the problem under ...
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### Implicit and Explicit finite difference discretization of steady state heat conduction equation

I understand what an implicit and explicit form of finite-difference (FD) discretization for the transient heat conduction equation means. But I am not able to understand if it is possible to ...
1 vote
364 views

### FEA: Newton-Raphson algorithm for Dirichlet BC non-linear static analysis

I have a standard non-linear static problem to solve with FEA. I am applying displacement boundary conditions only, no external force. The equation to solve look like these: $K(u)u=R(u)$ Eq(1) The ...
1 vote
134 views

### Calculate surface area and outward normal of each face(non-planar) for a irregular hexahedron.

I am using the vector cross product to calculate each surface area and thus the outward normal. However, this approach fails when the surfaces are non-planar. So what is the best approach to calculate ...
46 views

### Temperature not changing in my code for 1-D heat equation: Explicit Scheme

I am trying to solve the following 1-D heat equation with provided boundary conditions using explicit scheme on Matlab. I have been trying to plot the results but I realized that my temperatures are ...
1 vote
4k 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 ...
1 vote
37 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 ...
787 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 ...
41 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 ...
468 views

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 ...
1 vote
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### 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 ...
1 vote
16 views

### 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 ...
3k 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: ...
1 vote
2k 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 ...
1k 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 ...
3k 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 ...
1 vote
60 views

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

Is there any suggestion on sliding surface state derivative matrix (ds/dx) format? ...
120 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 ...
1k 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 ...
1 vote
45 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 ...