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Questions tagged [finite-volume]

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

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How well do finite volume methods ensure that no flux flows perpendicular to the flux vector?

Finite volume methods find approximate solutions to equations of the form: $$\frac{\partial \vec{u}}{\partial t}+\nabla\cdot(\vec{f}(\vec{u}))=0.$$ My question is has anyone done any analysis on how ...
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48 views

Finite difference method for conservative form of equations

My question is about how do we discretize the equations in the conservative form using finite difference method. I'm trying to solve Euler equations in conservative form. $$ \frac{\partial u}{\...
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42 views

How to discretize continuity equation with velocity calculated using Darcy's law?

$$ \partial_t(\epsilon_g\rho_g)+\partial_x\cdot(\epsilon_g\rho_g\mathbf{v}_g)=\Pi $$ I want to program normal continuity equation and Darcy's law to calculate velocity. $$ \mathbf{v}_g=-\frac{1}{\...
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2answers
56 views

TVD for temporal dicretisation

I have come across schemes where TVD (with flux limiters) is used for spatial discretisation along with Runge-kutta for Temporal discretisation. Can TVD be used for Temporal discretisation? If so ...
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1answer
39 views

Strain from FEM simulations to strain gauge measurements

I am looking for some intuition in making comparisons of FEM simulations to experimental measurements. In particular, I am interested in comparisons to strain gauge readings, and perhaps even LVDTs. ...
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1answer
79 views

Grid dependence of a numerical model

Statement of the problem Suppose, we consider the following model $$ \begin{array}{l} (1)~\mathbf{u}_t + \mathbf{F(u)}_x = \mathbf{S}(\mathbf{u},\mathbf{w}), \\ (2)~\mathbf{w}_x = \mathbf{P}(\mathbf{...
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41 views

Thermal stress to displacement through finite volume method

I am attempting to solve for a displacement field where I know the thermal stresses on my discretized domain, which consists of hex cells. My first question is: is easier way to solve for the ...
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41 views

Roe Riemann solver for perfect gas mixture

I have working program for solving one-component 1D Euler equations with Roe's approximate Riemann solver constructed according to this pdf. My implementation of the algorithm is as follows ($\rho$ is ...
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1answer
66 views

Exact Riemann solver for perfect gas mixture: problem with Newton's method convergence

I'm trying to solve multicomponent Euler equations for perfect gas mixture with Godunov-like scheme using exact Riemann solver. Of course, some approximate solver would probably be more cost-effective,...
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2answers
74 views

Elliptic equation with finite volume and unstructured high order geometry

I have found that in unstructured mesh, discretizing the laplacian operator with finite volumes requires special care, as given in An Introduction to Computational Fluid Dynamics: The Finite Volume ...
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0answers
38 views

WENO methods: why the characteristic wise method resulting big errors?

I was doing my research/project using WENO as the limiter in finite volume methods to solve hyperbolic conservation law. I have no idea why the result in the characteristic wise method has a big error ...
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1answer
61 views

TDMA with 3rd order upwind scheme

I'm trying to implement a model I found in a paper, but there is something I do not understand. The authors say they use TDMA to solve their equations; however, they use a 3rd order upwind biased ...
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49 views

Harmonic average of Diffusion Tensors in Finite Volume Method

I want to implement a Bilinear Finite Volume discretisation of the anisotropic diffusion problem: $$\frac{du}{dt} = \nabla \cdot (\textbf{D} \nabla u)$$ Both my degrees of freedom as well as the ...
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62 views

Oscillations in force coefficients from CFD simulations

I have carried out a CFD simulation (with finite volume method) to investigate the unsteady force enforced to the vehicle body. The horizontal tail keeps flapping in sinusoidal function. As a result, ...
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79 views

Basic approach for numerical solution of PDE

I'm looking for some guidance on how to write a program to numerically solve a PDE. As an example for comparison in 1D: $$\frac{d^2u}{dx^2} = f\;\;\;\;u(0) = 0\;\;\;\;u(1) = 0$$ We could try 6 ...
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1answer
22 views

Calculating volume of a discretised diffuse interface object

Suppose I have a spherical object projected onto a discrete square mesh. The dicretised circle can be represented by filling a logical matrix such that voxels in the interior of the sphere are filled ...
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1answer
37 views

Solving the diffusion/heat equation for a randomly distributed set of points in 3D

In this problem I am trying to solve, I have a messy set of points distributed in 3D space, each with a defined temperature. If I would want to calculate the heat transfer scenario in this system, how ...
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1answer
82 views

Does the PDE hold at every cell in a FVM mesh?

If you solve a given PDE (Navier stoke's, Euler, heat eqn, advection eqn, etc...) using FVM, is this PDE supposed to be valid at every cell in the discretized domain, or only in the global domain as a ...
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39 views

Jacobian Elements for Coupled Drift-Diffusion System using Vertex-Centered Finite Volume

I'm trying to solve the fully coupled drift-diffusion system using Newton's Method. Although I eventually plan to potentially use a Jacobian-Free Newton-Krylov approach, this is still something that I ...
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122 views

Finite Element Stabilization for Drift-Diffusion/Advection-Diffusion Equations

I've tried my best to look through the relevant suggested similar questions when posting this, and hopefully this contains enough new material to not be considered a duplicate. I'm currently trying ...
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125 views

Should ghost cells/nodes be coupled?

This is more of a theoretical question regarding the concept of ghost cells. When handling Neumann boundary conditions, ghost cells (in FVM) or nodes (in FD) are typically introduced. Essentially, ...
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1answer
101 views

Numerical Lax-Wendroff scheme order of convergence on Burgers equation

I was suggested to move that question here. The question to be as follows. Statement of the problem Is it possible to achieve the second order of convergence (OOC) of Lax-Wendroff (LxW) scheme ...
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1answer
48 views

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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79 views

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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35 views

Convergence rate assesment in space/time

I am solving a hyperbolic PDE (e.g. the shallow water equations) which depends upon $x$ and $t$. Typically, the overall convergence rate is calculated by comparing the numerical error in different ...
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5answers
203 views

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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54 views

Discretization used for steady linear elasticity - followup to previous question

This is a follow-up of my previous scicomp question (https://scicomp.stackexchange.com/posts/28863/edit). I figured I'd start a new thread on this as the question is a bit different from my previous ...
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1answer
85 views

Finite-volume method applied to a particular advection equation

I'm trying to apply the finite-volume method (FVM), with which I'm not so familiar, so a simple 1D PDE equation. I already asked this question in the math stackexchange, but was told that it could be ...
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1answer
255 views

Finite volume software packages

There are many software packages for the finite element method, of which the most popular are listed e.g. on Wikipedia. When it comes to the finite volume method, I'm not aware of any similarly ...
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0answers
121 views

Odd-even decoupling at faces of cells

I am currently solving PDEs using the finite volume method. The surface integrals of the equations that I am solving involves computing face gradients. The current algorithm that we use to compute ...
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0answers
80 views

FiPy with derivative source terms

I have a coupled nonlinear PDE system in 1 spatial dimension, in which I want to solve using FiPy. The dependent variables are $n$ and $T$: \begin{align} \frac{\partial n}{\partial t} \,&=\, D\,\...
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1answer
258 views

Crank-Nicolson method and mixed derivatives

I am curious if anyone had literature references or knowledge on how to apply the Crank-Nicolson (with approximate factorization) to the $$ \nabla \cdot (\nu (\nabla \mathbf{u} + \left(\nabla \mathbf{...
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2answers
232 views

Finite Difference and Finite Volume as special cases of Finite Element

I have heard this many times that "FD is a special case of FE" and separately, that "FV is a special case of FE". However I have never come across a brief document that substantiates that claim, ...
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64 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-...
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65 views

Reconstruction of cells information when given mesh in polyMesh format

The polyMesh format used in OpenFOAM is an intelligent format for which 'cells' file, i.e. the file giving list of nodes that make a cell, is not needed. The way to reconstruct geometry data such as ...
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1answer
202 views

Why is the continuous Galerkin Finite Element Method a poor choice for the inverse problem for the Navier-Lame equation?

I work in a field (elasticity reconstruction) that frequently uses standard Finite Element methods to solve the first order PDE, where we are given u and solve for mu and lambda: $$ (\mu(u_{i,j} + u_{...
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1answer
165 views

Computing Roe's average density for General Equation of State

I am solving a 1d Shock tube problem of compressible fluid obeying Euler equations(Hyperbolic pde). I am trying to simulate it using Finite Volume Method using Roe's Scheme. Half of the tube contains ...
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167 views

What can be done with Finite Element Method and not with the Finite Volume Method, and vice versa?

What are some applications where you would absolutely go for either FEM, but not FVM, or vice versa? What are some applications where both methods are equally suited? I worked with the FEM so far and ...
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2answers
124 views

If a numerical solution remains constant for different grid sizes, what does it mean?

I'm testing a finite volume scheme, Godunov type solver, using a problem with analytical solution. I'm not able to reproduce the solution, which includes source terms. I tried with different mesh ...
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40 views

Simulation of 2D impulse response using finite volume

Finite volume methods can be used to simulate the acustic wave equation (linearized Euler equations) in complex domains. I have developed a FV and a Discontinuous Galerkin code for 2D acoustic ...
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2answers
94 views

Halo Region Communication in Unstructured Mesh Problems

I'm currently using ParMETIS and it is required to determine the halo region of the local elements in a parallel unstructured mesh. Assume that the mesh is large and cannot be stored on a single ...
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0answers
50 views

FEM/FVM/FD for structural modeling and stability issues due to large structural constants?

I've read that in modeling structures problems, the finite element method (FEM) is typically used. I am unfamiliar with FEM, but I am wondering, in particular, if using FEM, as opposed to finite ...
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2answers
740 views

1D heat conduction using FVM in polar coordinates

I am trying to solve a 1D transient heat conduction problem using the finite volume method (FVM), with a fully implicit scheme, in polar coordinates. The governing equation is written as: $ \frac{\...
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0answers
178 views

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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0answers
230 views

Matlab CODE of ADER scheme [closed]

I read ADER WENO Finite Volume scheme for hyperbolic conservation laws with source term. I want to implement this method in Matlab coding. I got some problems in coding during to computation of ...
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0answers
499 views

Periodic Boundary conditions for 2D Euler equations

I am currently writing a 2D hydrodynamics code that simulates the 2D Euler equations using the AUSM method (Meng Sing Lou). I have tested the code on various 2D Riemann problems with Neumann ...
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1answer
210 views

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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197 views

How to impose Neumann boundary conditions in finite volume problems?

I'm trying to better understand finite volume methods and have started coding up a basic script to solve the diffusion equation $$u_t = u_{xx}$$ which has the finite volume form: $$\frac{\bar{u}^{n+1}...
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0answers
146 views

Spurious oscillations in diffusion-reaction problems with finite volume

I have successfully solved the multi-species diffusion-reaction equation \begin{equation} \frac{\partial c_i}{\partial t} = \nabla \cdot (d_i(x)\nabla c_i) + s_i(x,t), \quad \quad (1) \end{equation} ...
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1answer
89 views

If I discretize a PDE in space with WENO and in time with an implicit method, do I need to solve a nonlinear algebraic system at each time step?

I am attempting to solve a nonlinear advection diffusion equation $$\frac{\partial u}{\partial t} = \frac{\partial}{\partial x}(\frac{\partial u}{\partial x} + u^2)$$ with Robin boundary conditions ...