Linked Questions

58 votes
3 answers
5k views

Is manual adjustment of AccuracyGoal and PrecisionGoal useless?

This is a problem confusing me for years. AccuracyGoal and PrecisionGoal are two options that I never truly understand and, to ...
xzczd's user avatar
  • 65.4k
25 votes
2 answers
3k views

I failed to solve a set of one-dimension fluid mechanics PDEs with NDSolve

The fluid here has been assumed as single component perfect gas i.e. it obeys the equation $p=ρ R T$, the thermal conductivity is assumed as a constant, so the equation set is: ...
xzczd's user avatar
  • 65.4k
12 votes
4 answers
1k views

Solving Burger's equation with NDSolve at large time

I want to solve the following Burger's equation $$\partial_tu+\partial_x\left(\frac{u^2}{2}\right)=0,~~x\in[0,2\pi],~t>0\\u(x,0)=\frac{1}{3}+\frac{2}{3}\sin(x)$$ with mathematica. Here's my code: <...
Ho-Oh's user avatar
  • 245
19 votes
1 answer
2k views

How to solve the tsunami model and animate the shallow water wave?

Backslide introduced in 9.0, persisting through 13.1. Recently when I was learning differential equations, I noticed there is a shallow water wave equation to model the tsunami propagation. How to ...
LCFactorization's user avatar
10 votes
1 answer
931 views

Circumvent NDSolve::bdord: error for 1-D Euler Equations

I attempted to use NDSolve for the 1-D isentropic unsteady flow equations with low subsonic inflow velocity and prescribed inflow total enthalpy; along with a non-...
P. D. Thomas's user avatar
5 votes
3 answers
315 views

Problems with solving PDEs

I am using NDSolve to solve the two equations: ...
user55777's user avatar
  • 671
4 votes
1 answer
698 views

Solving a system of partial differential and algebraic equations? setting the step-size to get reasonable results

I'm trying to use Mathematica to get some early approximate solutions to a system of algebraic and partial differential equations. It is actually 1D model of an ideal gas in a tube. I'll divide my ...
Foad's user avatar
  • 605
3 votes
2 answers
436 views

how to fix this PDE numerical solution (NDSolve)

I have the following code: ...
user56834's user avatar
  • 545
5 votes
1 answer
488 views

Problem Solving Steady-State Euler Equations in 2D Using FEM

I am working with gas flows, and my Reynolds number is very large (>10^6). Still as a toy exercise, I solve the steady-state Navier Stokes equations for my volume and it seems to work ok for Reynolds ...
Paul Harrison's user avatar
1 vote
1 answer
220 views

Solving 3 nonlinear, transient, coupled PDEs [closed]

I'm trying to solve the fluid equations, continuity equations for mass, momentum, and energy, for a transient shockwave in 1D planar geometry. A piston is traveling at some velocity $u_p$ where $u_P$ $...
Liam's user avatar
  • 21
0 votes
0 answers
160 views

Problem with definition of boundary problem

My procedure for solving coupled 1 + 1 (spatial + temporal) PDE system: (Note: I have graphs of the correct solution with which I compare my result. See figure below text.) 1) I determine the ...
Vrbic's user avatar
  • 75
0 votes
0 answers
90 views

Need a method to solve a nonlinear PDE with gradients of the same order as the PDE's

I have a system of first order non-linear PDE's, but some of my boundary conditions are also of first order, so mathematica cannot solve it. When I looked online for similar problems , I found some ...
Hidde Rinsema's user avatar