Construction of Solutions for Two Dimensional Riemann Problems
Construction of Solutions for Two Dimensional Riemann Problems
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2) thus states that the vector [l, 5/«^«-), v^«")].
where is a tangent vector at the point of jump t, x, y. However, by the self -similarity of the Riemann solution, the vector [ 1, x/t, yit ] must also be tangent to the point of discontinuity. Consequently, the vector [ 0, x/r - 5/«^«-), yit - 5/u^«-) ] (2. 3a) is tangent to the point of discontinuity. In the plane f = 1, (2. 3a) has the simple form -6- [ 0, X - 5/u*, «-). Y - 5, («+, «-) ] . (2. 3b) Let a > b. Consider all planes passing thro...ugh the points (1, Sy(a, b), Sg(a, b)) and the origin (0, 0, 0). Parametrize the straight lines thus defined in the f = 1 plane (these are just the lines along the vectors (2. 3b)) by the angle 9, measured positive in the c»unterdockwise sense from the x-axis, with the straight line oriented as shown in Fig. 2. 1 . The normal (pointing from the b side to the a side) to each plane is given by n - (n„ n„ «^. ) = ± ( S/, a, b) tan 6 - Sgia, b), -tan 9, 1 ), (2. 4) where the + sign is used for --^ s 9 ^ -^ and the - sign for -^ ^ 9 ^ -^ .
What to read after Construction of Solutions for Two Dimensional Riemann Problems?
You can find similar books in the "Read Also" column, or choose other free books by W Brent Lindquist to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
2) thus states that the vector [l, 5/«^«-), v^«")].
where is a tangent vector at the point of jump t, x, y. However, by the self -similarity of the Riemann solution, the vector [ 1, x/t, yit ] must also be tangent to the point of discontinuity. Consequently, the vector [ 0, x/r - 5/«^«-), yit - 5/u^«-) ] (2. 3a) is tangent to the point of discontinuity. In the plane f = 1, (2. 3a) has the simple form -6- [ 0, X - 5/u*, «-). Y - 5, («+, «-) ] . (2. 3b) Let a > b. Consider all planes passing thro...ugh the points (1, Sy(a, b), Sg(a, b)) and the origin (0, 0, 0). Parametrize the straight lines thus defined in the f = 1 plane (these are just the lines along the vectors (2. 3b)) by the angle 9, measured positive in the c»unterdockwise sense from the x-axis, with the straight line oriented as shown in Fig. 2. 1 . The normal (pointing from the b side to the a side) to each plane is given by n - (n„ n„ «^. ) = ± ( S/, a, b) tan 6 - Sgia, b), -tan 9, 1 ), (2. 4) where the + sign is used for --^ s 9 ^ -^ and the - sign for -^ ^ 9 ^ -^ .
What to read after Construction of Solutions for Two Dimensional Riemann Problems?
You can find similar books in the "Read Also" column, or choose other free books by W Brent Lindquist to read onlineMoreLess
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