Questions tagged [finite-volume]

Referring to the discretization of partial differential equations using Finite Volume Method.

Filter by
Sorted by
Tagged with
1
vote
0answers
194 views

Do collocated grid arrangements definitely result in the checkerboard effect?

I understand the checkerboard effect due to the use of collocated grid arrangements in FVM. However, I wanted to know whether this problem is definitely bound to effect the results? For instance, I ...
1
vote
1answer
230 views

Are FEM or DGFEM methods based on integrals or PDEs?

I know that FVM is based on the integral form of conservation laws, and FDS is based on PDEs. What I'm confused by, is whether FEM and DGFEM formulations are based on integral or pde form of ...
1
vote
0answers
92 views

problem with understanding the fluid boundary conditions of a 1D probelm

I am having problems understanding the boundary conditions of the problem described in this paper on researchgate Essentially the problem consists of a one dimensional fluid chamber in contact with a ...
2
votes
1answer
92 views

Use of structs in Axisymmetric Finite Volume method

This might be better somewhere else, but I'll give it a try here first. I'm implementing a finite volume scheme for an axisymmetric problem in C, and am looking for a more efficient way to handle all ...
1
vote
1answer
586 views

Diffusion with space dependent drift in Fipy

I need to solve a diffusion equation in periodic boundary conditions using fipy but I would like to have a drift term that depends on the position so like this: $$ \partial_t u(x,t) = \partial_x^2 u(x,...
2
votes
1answer
394 views

MAC Projection in Projection method?

My question concerns the following paper: A Conservative Adaptive Projection Method for the Variable Density Incompressible Navier–Stokes Equations (http://www.sciencedirect.com/science/article/pii/...
1
vote
2answers
271 views

Dirichlet BCs - alternative implementation methods

I am having problems with solving a hyperbolic wave problem with Dirichlet BCs. I have tried reducing the time step sizes, which does not affect the results, and notices increasing the number of nodes ...
1
vote
0answers
54 views

should boundary conditions be effecting moving mesh results?

I have a question on the use of moving mesh to solve the inviscid euler equations. I have solved the following equations: $$\frac{\partial}{\partial t}\left[\begin{array}{c} \rho\\ \rho u \end{array}\...
0
votes
1answer
121 views

How to define fluxes for two dimensional convection-diffusion equation?

I want to solve the following differential equation using control volume approach on a Cartesian mesh: $$\frac{\partial T}{\partial t} + \frac{\partial T}{\partial x} + \frac{\partial T}{\partial y}= \...
2
votes
1answer
244 views

FVM - virtual node discretisation

I have come across the paper titled: A monolithic fluid structure interaction algorithm ... For a 1D grid, at the boundaries the paper uses virtual nodes $x_{0}$ and $x_{N+1}$ (page 372) and for ...
1
vote
0answers
164 views

Discontinuity at Interface

The equation at the left of the interface is \begin{equation} \displaystyle\frac{\partial C_i}{\partial t} = D_i \nabla^2 C_i - z_i \frac{D_i}{RT}F \nabla \cdot (C_i \nabla \phi_2) \end{equation} ...
4
votes
1answer
413 views

linear stability analysis using spectral radius

I am analysing the stability of a series of 1D linear equations of the form \begin{equation} \frac{d}{dt} x = A x \end{equation} discretised using upwind and central finite volume methods, etc, with ...
5
votes
1answer
198 views

Flux at coarse-fine mesh grid interface?

I am trying to solve one dimensional inviscid Burger's equation using adaptive mesh refinement. This is the PDE: $$\frac{\delta U}{\delta t} + \frac{\delta F}{\delta x} = 0$$ where the flux F of the ...
5
votes
0answers
170 views

Is it generally unstable to use in multidimensional simulations finite difference schemes with higher orders than 2?

I'm part of a team trying to generalize a 1D Advection-Diffussion-Reaction code we inherited by extending it to 2D by using dimensional splitting, i.e. solving advection and diffusion for x and y ...
4
votes
1answer
137 views

transverse component for multidimensional advection in method of lines

So I inherited from some people a code that solves the advection-diffusion-reaction equation for a particular system. The original code was first implemented in 1D which worked fine in cartesian ...
4
votes
2answers
2k views

The meaning of conservative discretization in Galerkin FEM and Discontinuous Galerkin

I do understand the meanning of "conservative discretization" within the FVM/FDM framework, indeed it is well explained in this post. Now, according to the table in this slide (pp.8), it concludes: ...
4
votes
1answer
70 views

Estimating the local compression/expansion ratio for a transformation on a point cloud

Let's say we have an unorganized point cloud P1 with N points, each with coordinates {x,y,z}. We apply non-rigid transformation to P1 (translation + rotation + warping), to obtain point cloud P2. ...
3
votes
1answer
775 views

Add User-defined/custom differential equations in OpenFoam (CFD)

I am new to OpenFoam. And I am trying to add a set (user defined) of differential equations to OpenFoam. I want to solve this user defined set of equations at each time point in addition to standard ...
2
votes
0answers
813 views

What is the difference between SSPRK3 and RK3 time discretization methods?

Here, SSPRK3 refers to third order strong stability preserving Runge-Kutta and RK3 refres to regular third order Runge-Kutta method. The meaning of the method is obvious from the name. However there ...
0
votes
1answer
1k views

Temperature dependent 1-d conduction in Python?

I'm trying to write a Python code that is a numerical solver for 1-d heat conduction (using FVM) with a temperature dependent thermal conductivity. The solver has three functions I need to iterate ...
1
vote
1answer
194 views

What does "strongly conservative" mean in the context of numerical methods?

I have a homework problem that asks me to show that 1st order unwinding or central differencing can give a strongly conservative, consistent scheme for the 1-D Burger's Equation using a finite volume ...
4
votes
2answers
576 views

Manufactured solution for pressure based 3d incompressible Navier-Stokes solver with wall boundaries

I already successfully verified my solver (SIMPLE-type FVM-method) with the following manufactured solution (3d Taylor-Green vortex) on the solution domain $[-1,1]^3$ with Dirichlet boundary ...
2
votes
0answers
134 views

Arbitrary Choosing of the Solution Domain - Navier Stokes and Manufactured Solutions

I want to verify a finite-volume solver (SIMPLE-Algorithm) for the incompressible Navier-Stokes equations by using a manufactured solution. I use Dirichlet boundary conditions for the velocity at all ...
2
votes
1answer
107 views

Application of CLAWPACK to Richards' equation

I'm looking to solve the Richards' equation. This models water flow in porous media and is a nonlinear, possibly degenerative, parabolic differential equation that takes the form $\partial_t \Theta(\...
2
votes
1answer
225 views

Unable to validate the Roe matrix for the Shallow Water Equations

In LeVeque's Finite Volume Methods for Hyperbolic Problems, p. 320-321, one may find the derivation of the Roe matrix to the 1D Shallow Water Equations (SWEs). It is $$ \hat{A}_{i-1/2}=\begin{pmatrix}...
2
votes
1answer
322 views

Finite volume method implementation issues

I am trying to write a simple finite volume method code but there are some concepts I'm still not really getting right (perhaps I'm overcomplicating things) Given a uniform grid, the idea is to ...
1
vote
2answers
195 views

Finite Volume Method flux integration

I was reading through this document about FVM. I understood all up to the point where we have on page 15 the following $$(\bar u^{n+1}_i - \bar u^n_i) \Delta x + \int^{t^{n+1}}_{t^n} f(u(x_{i+1/2},t))...
1
vote
1answer
290 views

What kind of test cases are convenient to use for testing the code for Euler equations of gas dynamics in polar coordinates?

Consider Euler equation of gas dynamics in polar coordinates as $$ \left( \begin{array}{ccc} \rho \\ \rho u_{r} \\ \rho u_{\theta} \\ E \end{array} \right)_{t} + \frac{1}{r} \left( \begin{array}{ccc}...
3
votes
0answers
369 views

Euler Equation Eigensystem with Gravity in the Energy Flux

I am modifying a conservative form of the Euler equations with gravity in the energy flux (see previous question: Energy Conservation in Conservation Laws with Source Terms) for use in a Riemann ...
3
votes
2answers
424 views

Energy Conservation in Conservation Laws with Source Terms

I'm wondering if anyone can help me understand energy conservation when using conservation law methods (i.e. Riemann solver, High-Resolution Wave-Propagation Methods) with the addition of source terms:...
4
votes
1answer
1k views

Numerically solve a PDE in Python with a term calculated by coarse-graining

I'm trying to solve a PDE in Python of the form, $\dfrac{\partial c(\mathbf{x}, t)}{\partial t} = \mathrm{D} \nabla^2 c(\mathbf{x}, t) -\gamma \rho(\mathbf{x}, t) c(\mathbf{x}, t)$ where $c$ ...
1
vote
1answer
82 views

Accurate dot-product of fields with only knowing normals

I am trying to accurately calculate $\vec{j} \cdot \vec{E}$ for an electron energy equation on a finite-volume mesh. $\vec{j}$ is the electron current density, and $\vec{E}$ is the electric field. ...
2
votes
2answers
188 views

Is there a bound on the number of edges, facets, and elements in a 3D simplicial mesh in terms of the number of mesh nodes?

I am currently working on a 2D finite element code with a mesh that contains duplicate nodes at certain interfaces where jumps occur. In order to set up the appropriate linear systems, I have to take ...
3
votes
2answers
221 views

Finite element: handle discontinuity/abrupt interface

I am using Galerkin's method to set up some pde solver for my problems(1D/2D) at hand. Some abrupt material interfaces do exist, so far, what I did regarding this is simply: 1) no element across the ...
2
votes
0answers
186 views

boundary conditions with non-constant coefficients in cell centred finite volume method

Suppose am solving the heat conduction equation in 1d with Dirichlet boundary conditions. The thermal conductivity $k$ is a non constant function. So $-(k(x)u'(x))' = f(x)$ The value of $k$ enters the ...
4
votes
1answer
3k views

Comparison of Lattice Boltzmann Method vs Traditional Navier-Stokes based Methods

I have a choice of two options, analysing and implementing Lattice Boltzmann methods or traditional Navier Stokes based methods. I'm a CFD newbie and I have a rough idea (though not rigorous enough to ...
2
votes
1answer
435 views

Moving airfoil boundary conditions

I am trying to simulate a moving airfoil with constant speed (Mach=0.755, aoa=1.25). I solve Euler equations with Roe's method. I have two boundary conditions: Farfield Slip wall (airfoil) For all ...
2
votes
0answers
407 views

finite volume for diffusion equation with anisotropic (tensor) coefficient

Consider the scalar PDE for $u$ with Dirichlet boundary conditions: $\mathrm{div}(\mathcal{K}\nabla u) = f\; \forall x\; \in \Omega \subset R^2$, $u = 0 \; \forall \; x\;\in \partial\Omega$ ...
5
votes
0answers
88 views

Interface Formulation at Finite Volume Boundaries when using the Dual Mesh

When using the dual mesh (vertex-centered) for finite volume methods, you end up with a cell center at the boundaries between materials. It is possible that the equations being solved in each ...
3
votes
2answers
477 views

data structures for efficient/easy implementation of finite volume method for 2D Poisson equation

My question is about implementation alone. Consider a square domain with regular square, cell centred finite volumes. This is for the multiscale finite volume method (Jenny and Lunati) I need to ...
2
votes
1answer
507 views

Assembling sparse matrix in PETSC for Poisson equation

I am a novice at PETSC, and I have been trying to write an FVM code for steady heat conduction in 2D using PETSC (square, regular grid, Dirichlet boundaries) Since the large matrix , say A, will be ...
4
votes
2answers
3k views

Developing finite volume (FVM) code in C . General advice

I need to develop a FVM code in C (The multiscale FVM method for heterogeneous media). I know that: Only uniform rectangular grids will be considered (2d now, later 3d) Sparse systems will be large ...
1
vote
1answer
801 views

Euler's equations 1d for pipe, Inlet boundary conditions

$\def\rmin{{\mathrm{in}}}$ $\def\l{\left}\def\r{\right}$ $\def\tagl#1{\tag{#1}\label{#1}}$ I am using the one-dimensional finite volume method to calculate the air flow in some tube. For subsonic ...
3
votes
1answer
120 views

Conservative FV Immersed boundary method for compressible flow

Is there a conservative FV second-order (or first-order) accurate immersed boundary method for compressible flow including moving boundaries (in the literature)? By compressible flow I mean the ...
7
votes
1answer
275 views

Implementation of convection scheme given by normalized variable diagram

In finite difference and finite volume methods, convection schemes (upwind, central, quick, ...) are usually shown in a normalized variable diagram. The diagram gives the normalized face variable as a ...
5
votes
0answers
477 views

Finite volume method

I have question connected with finite volume method. Consider equation $$\frac{\partial u}{\partial t}=\operatorname{div}A\nabla u +f . \quad x\in \overline{B}_{1} (0)\subset \mathbb{R}^3 -\text{unit ...
0
votes
2answers
351 views

Reconstructing fluxes [closed]

Given a standard advection equation, we write the update as $$ q_i^{n+1}=q_i^n+\frac{\Delta t}{\Delta x}\left(F_i^{n+1/2}-F_{i+1}^{n+1/2}\right) $$ with $F_i^{n+1/2}=F\left(q_i^n,\,q_i^*\right)$ and $...
5
votes
1answer
1k views

Finite Volume Implementation

I am trying to implement a simple finite volume method solver. I had a class on FVM a while back, but am still aware of the principal concepts. But implementing the FVM for non-cartesian or 1D meshes ...
1
vote
0answers
211 views

Characteristic length of differential element of cylinder surface?

I am trying to find the Nusselt number for a small element of the outside of a cylinder that has a height of $\Delta z$. I found the average Grashof number of a surface as $$Gr_{L}=\frac{\beta \rho (...
1
vote
0answers
190 views

Problem with cell size and boundary conditions in transient cylindrical conduction

I am attempting to model the steady state behavior of a cylinder using the finite volume method (FVM) subjected to a variety of boundary conditions in Matlab. First off, I am treating the cylinder as ...