Questions tagged [hyperbolic-pde]

Hyperbolic partial differential equations describe wave behavior.

116 questions
Filter by
Sorted by
Tagged with
63 views

TVD Lax-Wendroff with non-constant velocity

I am dealing with a linear advection equation with a non-constant velocity, where I would like to apply a TVD Lax-Wendroff scheme in 1D. The equation is the following: \frac{\...
72 views

63 views

I'm trying to do discretization to the following system: $\frac{{\partial \rho }}{{\partial t}} = - \frac{{\partial \rho }}{{\partial x}}u - \rho \frac{{\partial u}}{{\partial x}}$ $\frac{{\partial ... 1answer 112 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 ... 3answers 293 views When is it safe to ignore the diffusion term in an advection-diffusion equation? Given the one dimensional equation:$\epsilon\frac{\partial^2u}{\partial x^2} +\frac{\partial u}{\partial x} = 0 $with$0\le\epsilon \ll1$with boundary conditions$u(0) = 0$and$u(1) = 2$, we ... 0answers 141 views Good numerical method for solving the Kadomtsev Petviashvili equations. Is there an analytical solution? I need to solve the Kadomtsev Petviashvili (KP) equations $$\partial_x(\partial_t u+u \partial_x u+\epsilon^2\partial_{xxx}u)+\lambda\partial_{yy}u=0$$ where $$\lambda=\pm 1 \;.$$ My questions ... 2answers 939 views Advice on numerical solution for 2D hyperbolic PDE with zero flux boundary conditions I would like to numerically solve a hyperbolic PDE of the form$\frac{\partial\theta_t}{\partial t}(x,y)+\frac{\partial\left[\theta_t \gamma_t^x\right]}{\partial x}(x,y)+\frac{\partial\left[\theta_t \...
311 views

I would like to know which is the best way to integrate numerically Legendre polynomials. I am building up a Discontinuous Galerkin CFD code for which Legendre polynomials are used as basis functions ...