Questions tagged [grid]

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How to optimally choose points for multivariable Hermite interpolation?

I have a multi-variate, continuous function $f$ from $R^n$ to $R$, which I can query for its output for any input. I would like to create interpolation polynomial for it. In one-dimensional case ...
3
votes
0answers
54 views

What is the reason for this finite-difference high errors on non-uniform grid?

tl;dr Using a Taylor-matched method to find coefficients for the discretized equation $ \mathbf{A} \vec{f}'' = \mathbf{B} \vec{f} $, a Fortran code has been implemented to find the second derivative ...
3
votes
0answers
99 views

WENO5 scheme in a staggered grid

I'm trying to use the finite-difference WENO scheme to solve the 2D density conservation law with axial symmetry (coordinates $r,z$): $\frac{\partial \rho}{\partial t}+\nabla \cdot (\rho \vec{v}) = \...
1
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0answers
23 views

Solution errors when refining a static grid: Continuous vs. step-wise refinement

Let's assume I am working on a 2-D domain on $R^2$, with my coordinates $x \in[-1,1]$, $y \in[-1,1]$ and I want to solve a popular CFD problem, like the shallow water system or the Euler system. At $x=...
1
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0answers
17 views

Translating grid with extrusion speed

I am putting into MATLAB code the equations that describe a plastic extrusion process. From a paper, I found I should use a spatial grid that translates with the extrusion speed, being the reference ...
1
vote
0answers
90 views

Choice of velocity grid - staggered or not?

I'm trying to understand when and why one would use a staggered vs. a colocated grid in problems that have velocities and scalars that they transport (e.e. density). If scalars are defined cell-...
1
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0answers
55 views

adaptive / smart grid choice for dynamic programming

I've a read a paper about investing where they used a dynamic programming approach to solve a finite horizon problem, i.e. $$\max_{x_t} E[u(W_T)] $$ where $u$ is a utility function and $W_T$ ...
1
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0answers
133 views

C1 continuous spline on regular 2D-grid with quadratic 1D cuts

I want some scalar spline function defined on regular 2D grid $F(x,y)$ with continuous first derivative which is easy to intersect with arbitrary ray/line ${\vec l}(t) = (c_x t,c_y t,c_z t)$. ...
1
vote
0answers
118 views

Finding boundary intersection points with Cartesian grid?

I would like to find the intersection points e.g. $M_x$ and $M_y$ as in the attached figure. The boundary (solid line) is defined by the Lagrangian points. I am working in C++ (basic - medium ...
0
votes
1answer
53 views

Is it possible to resample grid in such a way so that continuous objects remain continuous?

Suppose I rasterize a rectangle of width 2.5 gridpoints and get the values as shown: =============== | 0 | 1 | 1 | 0.5 | 0 | Now I resample that ...
0
votes
0answers
32 views

Grids for atmosphere simulation with finite volumes on the globe

I am currently in the early construction process of building a simple CFD model of a rotating planetary atmosphere. The planet should be allowed to tilt significantly, so that a time-dependent source ...