# Questions tagged [discretization]

The process of representing a continuum space with a finite set of points/elements

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### Problems with deriving an equation for a finite-difference scheme given in the journal paper

I'm reading this paper and trying to follow everything that the author has done. A Comparative Study of Finite Volume Method and Finite Difference Method for Convection-Diffusion Problem But there ...
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### Monotone, monotonicity preserving, LED, TVD, NVD, bounded, stable and stability preserving discretization schemes [closed]

When it comes to discretization schemes for finite volume method, the following terms can be found in literature: monotone schemes monotonicity preserving schemes local extremum diminishing schemes ...
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### Don't we care about the numerical diffusion in the diffusion term?

In the context of the solution of advection-diffusion equations by finite volume method, many numerical schemes, papers and book chapters are dedicated to address the numerical diffusion and/or ...
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### How to account for the interface between two different phases in a discretized diffusion model?

I have tried to set up a model for the diffusion of a gas into a liquid. The two media are next to each other and the geometry is spherical because the system should simulate the diffusion out of a ...
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### Discontinuous Galerkin FEM : Control points are mid-points of edges instead of nodes

I am thinking to use discontinuous galerkin FEM (DGFEM) method to estimate discontinuous displacement field $u: \Omega \rightarrow \mathbb{R}^2$ at the crack surface of a material. The domain is ...
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### Implementation of stochastic cellular automata

In my problem, I have a lattice with a stochastic cellular automaton. In order to simplify a bit, let's say it is 1D. In my system, each node can be type A, B or C. A way to represent the system and ...
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### Can this nonlinear advection-diffusion equation be discretized as to only have to solve SPD systems?

Consider a nonlinear advection-diffusion equation of the form $$\frac{\partial u}{\partial t} = \nabla \cdot (a(u) \nabla b(u) - \vec{c}(u)u) \tag{1}$$ on a rectangular domain with Dirichlet ...
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### Implement Robin boundary condition (finite volume)

I have a PDE equation with Robin Boundary condition in an annulus system and I should solve it by finite volume method: \begin{align} \frac{\partial T_f}{\partial t} - k \left(\frac{\...
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### Discrete operator textbooks

This will be a vague question. When I was writing a finite element matrix assembly routine, a colleague noticed that I had a bug in my code because the sparsity pattern of the one of the blocks didn'...
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### Discrete wave simulation - absorbing boundaries?

I wrote a simple 2D wave simulation using the following equations: $$\frac{\partial^2 u}{\partial t^2}=c^2\nabla^2u$$ Where $\nabla^2$ is the discrete laplace operator using a Von Neumann neighborhood ...
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### Finite Volume Polar Discretization: Lengths

Given a uniform polar grid, as in the figure below: and a FV discretization of a gradient for example: $\frac{\partial p}{\partial \varphi} = 0$ $\Delta r \frac{p_e - p_w}{\Delta \varphi} = 0$ My ...
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### Literature on numerical solving based on multiple meshes?

Consider solving a differential equation system for 1D, 2D, or 3D. It involves various input and output "field" variables, which, more often than not, correspond to various physical quantities ...
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### Order of accuracy of FVM discretization

I've recently got interested in CFD and started a small project by solving the radial Reynoldsequation. Why the Reynoldsequation? I recently encountered it through my studies and somehow got stuck :) ...
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### Rhie and Chow Pressure Velocity Coupling

In a collocated grid, which velocity is used in the convective term in the momentum equation? Is the Rhie and Chow constructed face velocity or an average of the adjacent cell center values(in a ...
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### Three steps of pde numerical solution and nonlinear equation

I'm very new here. I'm trying to solve nonlinear elliptic equation $$(n(u)u')' = f(u)$$ and face with crucial misunderstanding. As I suppose, the procedure of solving some nonlinear equation ...
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### Space-time Galerkin of Burgers changes the convection speed

tldr: Can space-time Galerkin schemes applied to convection-diffusion problems lead to effects on the convection velocity? For time $t\in (0,1)$ and the spatial variable $\xi \in (0,1)$, I am ...
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### Motivation behind Collocation Method

In the previous question "Motivation behind Galerkin method", Paul gives a good and easy-to-understand explanation indicating that the Galerkin method is a kind of projection method. Can anyone ...
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### Second and Higher Order Order Corrector in Spectral Deferred Correction

I am trying to work out a second order or higher order correction for the method of Spectral deferred Correction (SDC). Specifically using as a corrector a second order or third order multi-step. In ...
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### High order unconditionally stable discretization for a scalar hyperbolic PDE

In order to numerically solve the following differential equation: \begin{equation} \text{Fr}\{f\} := v(k)\dfrac{\partial f(z,k)}{\partial z} - F(z) \dfrac{\partial f(z,k)}{\partial k} = -\dfrac{f-...
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### Second order interpolation scheme

On a grid I am having the values of a physical quantity say for example Temperature, at the E,W,N,S and P node all of them being calculated using a second order discretization scheme. I want a second ...
466 views

### How to define residual in multigrid approach?

I wish to solve the two-dimensional Navier Stokes equations using multigrid method on a collocated grid using the Predictor-Corrector method mentioned below. But first, let me elaborate on what I had ...
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### How to choose a good distribution for visualizing phase changes in the nature of the roots of a quadratic equation

I'm not sure if this SE site is the best one for this question, so let me know where it should be moved to if you think it doesn't belong here. After learning about the quadratic formula, I'm ...
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### Does scaling factor affect discretization?

Suppose I want to solve the below equation numerically. $$\frac{dy}{dx}=y$$ I'd like to normalize the space discretization by choosing $$a\bar{x}=x$$ where I assume $\bar{x}$ is unity. Then the ...
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