Nonuniform mesh with the numerical method of characteristics

In summary, The conversation is about finding a good book or article that describes how to use a coarse and fine spatial mesh with the numerical method of characteristics. Suggestions for books are Modern Compressible Flow: With Historical Perspective by John D. Anderson and Gas Dynamics by James E.A. John and Theo G. Keith. The person is using Matlab for their code and is unsure about how to move the fine mesh as the characteristics move. They also mention the importance of calculating points in characteristics codes and express interest in seeing the other person's code when finished.
  • #1
kobjob
7
0
Could someone please direct me to a good book/article that describes how to use a coarse and fine spatial mesh with the numerical method of characteristics?
Thank you.
Kate
 
Physics news on Phys.org
  • #2
The book Modern Compressible Flow: With Historical Perspective by John D. Anderson is good as well as Gas Dynamics by James E.A. John and Theo G. Keith.

What are you using to write your code? Fortran, matlab?
 
  • #3
Thanks for your suggestions!

I'm using Matlab. I'm not sure how/if I should be moving the fine mesh as the characteristics move.

Thanks again,
Kate
 
  • #4
The main thing with characteristics codes is calculating the actual points. You have a normal rectangular grid to begin with and then you have you characteristic mesh and you have to go from you characteristics mesh (where the values are exact) to your rectangular mesh where the values become approximate.

I wouldn't mind having a peek at your code when you're done.
 
  • #5


As a scientist familiar with numerical methods, I would recommend looking into the book "Numerical Methods for Conservation Laws" by Randall J. LeVeque. This book covers the use of nonuniform meshes in the numerical method of characteristics, as well as other numerical methods for solving conservation laws. Additionally, the article "Adaptive Mesh Refinement for the Method of Characteristics" by R. J. LeVeque, J. A. Rossmanith, and G. Warnecke provides a detailed explanation of using both coarse and fine spatial meshes in the numerical method of characteristics. These resources should provide a comprehensive understanding of how to use nonuniform meshes with the method of characteristics.
 

1. What is a nonuniform mesh in the numerical method of characteristics?

A nonuniform mesh is a discretization technique used in the numerical method of characteristics, which is a numerical method for solving partial differential equations (PDEs). In this method, the domain is divided into smaller elements or cells, and the solution is calculated at the center of each cell. Nonuniform mesh refers to a mesh where the size of the cells is not uniform, i.e., the size of the cells varies throughout the domain.

2. Why is a nonuniform mesh used in the numerical method of characteristics?

A nonuniform mesh is used in the numerical method of characteristics to improve the accuracy of the solution. In some cases, a uniform mesh may not accurately capture the behavior of the solution, especially near the boundaries or regions with high variation. By using a nonuniform mesh, the cells can be smaller in areas where the solution changes rapidly, leading to a more accurate solution.

3. How is a nonuniform mesh constructed in the numerical method of characteristics?

A nonuniform mesh is constructed by dividing the domain into smaller cells with varying sizes. This can be done manually by specifying the size of each cell or using an adaptive meshing algorithm that dynamically adjusts the size of the cells based on the solution behavior. The goal is to have smaller cells in regions where the solution changes rapidly and larger cells in regions with less variation.

4. What are the advantages of using a nonuniform mesh in the numerical method of characteristics?

There are several advantages of using a nonuniform mesh in the numerical method of characteristics. These include increased accuracy of the solution, reduced computational cost, and better capturing of solution behavior near boundaries and regions with high variation. Additionally, a nonuniform mesh can also improve the stability of the solution, as it can prevent large errors from propagating.

5. Are there any limitations or challenges associated with using a nonuniform mesh in the numerical method of characteristics?

One of the main challenges of using a nonuniform mesh in the numerical method of characteristics is the difficulty in constructing the mesh for complex geometries. In these cases, it may be challenging to determine the appropriate size and distribution of cells. Additionally, using a nonuniform mesh may also lead to increased computational cost and complexity in the implementation compared to a uniform mesh.

Similar threads

A Runge-Kutta: Maintaining Units in Numerical Methods
    • Differential Equations
Replies
16
Views
3K
On the cusp of fully grasping Method of Characteristics
    • Aerospace Engineering
Replies
1
Views
923
I The algorithms involved in finding a solution with numerical methods
    • Differential Equations
Replies
14
Views
2K
A Matrix Exponential to Approximate the Value of Matrizant
    • Differential Equations
Replies
2
Views
2K
A Implicit Euler method with adaptive time step and step doubling
    • Differential Equations
Replies
2
Views
4K
A Numerically solving a transport equation
    • Differential Equations
Replies
3
Views
1K
MCNP: mesh with weight window generator
    • Nuclear Engineering
Replies
2
Views
2K
Looking for resources to help me understand the basics of PDEs for physics
    • STEM Academic Advising
Replies
5
Views
611
A Lecture notes on Finite Difference Methods
    • Differential Equations
Replies
1
Views
3K
I Applications needing fast numerical conformal maps
    • Differential Equations
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top