Questions tagged [verification]

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Isolating bugs with convergence testing

Let's say that I have a numerical code and I'm doing convergence testing on the code. The code fails the convergence test, that is, the order of convergence is not as expected. Checking the order of ...
Ben Trettel's user avatar
2 votes
0 answers
72 views

How can I validate my time integration scheme for my dynamic linear elasticity FEM code with a manufactured solution or similar?

I am solving for a dynamic linear elasticity problem: \begin{equation} \dfrac{\partial^2 u}{\partial^2 t} - \nabla \cdot \sigma = f \end{equation} where $ u \in R^2 $ with sufficient BCs and ...
CuteCompute's user avatar
0 votes
1 answer
91 views

How are topology optimizations validated?

How are topology optimizations validated? I've been confused. Doesn't this mean that each of such design (e.g. N=100) would still need to be validated empirically or is there something that allows one ...
mavavilj's user avatar
  • 427
3 votes
2 answers
85 views

Setting up consistency tests in FVM

I am in need of some help to valdate a consistency test with a finite volume method solver. The idea is the following: Based on the method of manufactured solutions (MMS) I am supplying the analytical ...
Banana trick's user avatar
1 vote
0 answers
220 views

Confused on how Method of Manufactured solutions works?

I am new to computational science and I am trying to wrap my head around how MMS works. I am solving the time independent Helmholtz equation as a simple test of the technique so my starting equation ...
TheCodeNovice's user avatar
1 vote
1 answer
149 views

Which 2D PDE with an exact solution can I use to test/verify my FEM-PDE code?

I have created a program to solve 2D, time-dependent PDEs with the finite element method and get reasonable looking results for the 2D acoustic wave equation. Now I would like to go further and solve ...
Marten's user avatar
  • 231
0 votes
2 answers
98 views

Verifying convergence of a stationary solution to a PDE with the Runge-Kutta method

I am numerically solving a nonlinear wave PDE using the Runge-Kutta method, and I know the solution I am looking for is constant in time, but I do not know the solution. What is a good way of ...
VoidDragon's user avatar
7 votes
1 answer
274 views

Are there any drawbacks to using the Method of Manufactured Solutions for convergence testing?

Are there any drawbacks to using the Method of Manufactured Solutions for convergence testing and verification studies? I really can't think of any.
user27504's user avatar
  • 321
1 vote
0 answers
213 views

Method of manufactured solutions - choice of type of boundary conditions

I am attempting to use the method of manufactured solutions (MMS) for code verification for linear elasticity. However, this is more of a general question regarding the general use of MMS. In MMS, ...
user27504's user avatar
  • 321
1 vote
0 answers
92 views

Computational approaches to analyse numerical solutions

I apologise beforehand if the question isn't well defined or is too broad, I'm just having some difficulty finding the information I need. I also apologise if this should have been asked on stack ...
Matthew Cassell's user avatar
2 votes
2 answers
501 views

In practice, what are the most useful ways to visualize 2d fluid flow, to tell what is happening in the simulation? Esp for verification and debugging

My simulation creates a 2d grid of vectors and scalars (EDIT of velocity, depth etc), at 60 frames per second. Is it correct? It looks sort of right... but who knows? How can I tell what's happening - ...
hyperpallium's user avatar
0 votes
2 answers
186 views

What would be a simple approach to validate a wave propagation code?

I have a linear elastic wave propagation code and an elastoplastic wave propagation code based on FEniCS. For now, I keep the 2D mesh (100, 100) fineness unit square and give a source wave of $\sin(...
CRG's user avatar
  • 347
0 votes
1 answer
116 views

What should I put on the paper to show the correctness and convergence of my solution?

I am using FEM to do an assignment on a heat conduction problem on a complex domain, which needs me to get the variation of the temparature distribution subject to the variation of boundary conditions,...
user123's user avatar
  • 679
12 votes
2 answers
624 views

Verification in Eigenvalue problems

Let us start with a problem of the form $$(\mathcal{L} + k^2) u=0$$ with a set of given boundary conditions (Dirichlet, Neumann, Robin, Periodic, Bloch-Periodic). This corresponds with finding the ...
nicoguaro's user avatar
  • 8,500
5 votes
1 answer
316 views

Method of Manufactured Solutions for non-differentiable coefficients

The Method of manufactured is commonly used for verification of computational science codes. I want to use the method for verification of Navier-Cauchy (elasticity) equations with periodic and Bloch-...
nicoguaro's user avatar
  • 8,500
6 votes
1 answer
472 views

Guidelines for choosing manufactured solutions for numerical PDE schemes

When testing a numerical method for a PDE, I know that it's often useful to compare it to a known analytical solution. If none is available, one can always 'manufacture' a solution, substitute it ...
Paul's user avatar
  • 12k
10 votes
3 answers
2k views

manufactured solutions for incompressible Navier-Stokes -- how to find divergence-free velocity fields?

In the method of manufactured solutions (MMS) one postulates an exact solution, substitutes it in the equations and calculates the corresponding source term. The solution is then used for code ...
chris's user avatar
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