Finite Difference Methods for Hyperbolic Equations

Many problems in fluid mechanics, such as those in aviation, meteorology, oceanography, and water conservancy, come down to hyperbolic equations and hyperbolic systems. These problems are often nonstationary and nonlinear, coupled with viscosity, turbulence, and shock waves (discontinuous interfaces). The resulting complex phenomena make these problems particularly challenging to solve. Given that the complexity of the differential equations may obscure the essence of the numerical solution, this chapter focuses on finite difference schemes specifically designed to solve the wave equation. The convergence and stability of these schemes are also discussed.