Application of the Method of Fractional Steps to Hyperbolic Equations

N. N. Yanenko
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N. N. Yanenko: U.S.S.R. Academy of Sciences, Siberian Branch Computing Center

Chapter Chapter 3 in The Method of Fractional Steps, 1971, pp 42-53 from Springer

Abstract: Abstract Consider the equation of acoustics 3.1.1 $$\frac{{\partial u}}{{\partial t}} - {a^2}\frac{{\partial v}}{{\partial x}} = 0;\,\frac{{\partial v}}{{\partial t}} - \frac{{\partial v}}{{\partial t}} = 0,$$ where u is the velocity; v is the specific volume; a is the velocity of sound, and x; is the Lagrangian coordinate. Written in terms of Riemann invariants 3.1.2 $$r = u - av;\,s = u + av,$$ Eq. (3.1.1) takes the form 3.1.3 $$\frac{{\partial r}}{{\partial t}} + a\frac{{\partial r}}{{\partial x}} = 0;\,\frac{{\partial s}}{{\partial t}} - a\frac{{\partial s}}{{\partial x}} = 0$$

Keywords: Hyperbolic System; Hyperbolic Equation; Implicit Scheme; Order Accuracy; Fractional Step (search for similar items in EconPapers)
Date: 1971
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DOI: 10.1007/978-3-642-65108-3_3

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