# 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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### In FEM, what is the difference between a single element with a quadratic shape function and two elements with linear shape functions?

Using Finite Element Analysis to obtain a Weak form of a PDE, what is the difference between the two cases: A single element with a quadratic shape function Two elements with linear shape functions. ...
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### 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 ...
35 views

### Does numerical dissipation in FE simulations affect system's elastic energy? Does it depend on thickness?

I am running a finite-element simulation in Abaqus, for which I also have a theoretical model. To be precise, I am simulating wrinkling in a thin annular sheet, with shell elements. The model makes a ...
35 views

### Why is the amount of force/moment transfer occurring between bodies in FEA is independent of mesh size?

So I read somewhere that the mesh size won't effect the amount of force transfer occurring between bodies if several bodies are in contact, and a global force is applied somewhere. I wanted to know ...
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### What is the difference between Frictional non-linearity and Geometric non-linearity in FEA? (In terms of Stiffness matrix)

For geometric non-linearity, we know that as the geometry changes during the analysis, the global stiffness matrix changes since it already is a function of geometry of the structure. What I want to ...
48 views

### Errors obtained in the numerical solution of the 1D convection-diffusion equation

I have been trying to solve the 1D convection-diffusion equation In implementing the above, I have tried to follow closely the method described here: https://uk.mathworks.com/support/search.html/...
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### Analytical solution for the 1D convection-diffusion equation

The Ogata and Banks analytical solution of the convection-diffusion equation for a continuous source of infinite duration and a 1D domain: where C [mol/L] is the ...
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### Perfectly Matched Layer (PML) for Plates in COMSOL

I am modelling infinite plate domain in COMSOL for frequency simulation. I need to apply absorbing boundary conditions all around the boundaries and I could not find PML option for plates. Could ...
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### How are eigenvalues of a cell in the finite volume discretization calculated? (for euler fluid equations)

I am building a program to numerically solve the euler fluid equations based on finite volume discretization and am having trouble on a step where the eigenvalues of a cell need to be calculated ...
57 views

### 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 ...
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### Is it possible to measure the concrete workability by a mobile app one day? [closed]

After studying all methods that can measure the concrete slump, I found 62 devices that service this purpose at the same time these devices are expensive and not practical enough, for this reason the ...
130 views

### Does Finite Element Method use direct stiffness method?

Does Finite Element Method use direct stiffness method? Or it is another mathematical method? We definitely use direct stiffness method to solve frames. FEM is based on entirely this or depending on ...
85 views

### Analytical solution of thermal stress in a bi-metallic cylinder

As a side project I have looked to solve using Python an analytical solution for one-dimensional transient heat transfer in a thick cylinder with cladding on the inside surface, wherein the fluid in ...
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### Water distribution through N x Needle orifices

Consider a water distribution setup consisting of a feeder line blocked at one end but having 100 needle outlets all the same size. The feeder line cross sectional area is much greater than a needle ...
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### 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,...
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### Simufact / MARC and Fortran

I am using Simufact from MSC Software to perform numerical simulations. To be able to create my own sub-routines I need to have Fortran compiler installed. Simufact manual mentions only Intel Fortran +...
50 views

I am trying to write a python code to solve the neutron diffusion equation to model neutron flux distribution in a one-dimensional two-group setting. The governing equations of the system are: $$-... 1answer 64 views ### 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 ... 1answer 165 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 ... 1answer 94 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 ... 1answer 36 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 ... 2answers 2k 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 ... 0answers 34 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 ... 0answers 637 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 ... 0answers 37 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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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...