Conservation laws arise from the modeling of physical processes through the following three steps: 1) The appropriate physical balance laws are derived for m-phy- t cal quantities, ul""'~ with u = (ul' ... ,u ) and u(x,t) defined m for x = (xl""'~) E RN (N = 1,2, or 3), t > 0 and with the values m u(x,t) lying in an open subset, G, of R , the state space. The state space G arises because physical quantities such as the density or total energy should always be positive; thus the values of u are often con strained to an open set G. 2) The flux functions appearing in these balance laws are idealized through prescribed nonlinear functions, F.(u), mapping G into J j = 1, ..• ,N while source terms are defined by S(u,x,t) with S a given smooth function of these arguments with values in Rm. In parti- lar, the detailed microscopic effects of diffusion and dissipation are ignored. 3) A generalized version of the principle of virtual work is applied (see Antman [1]). The formal result of applying the three steps (1)-(3) is that the m physical quantities u define a weak solution of an m x m system of conservation laws, o I + N(Wt'u + r W ·F.(u) + W·S(u,x,t))dxdt (1.1) R xR j=l Xj J for all W E C~(RN x R+), W(x,t) E Rm.
Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables
RRP:
$237.29
Description
Conservation laws arise from the modeling of physical processes through the following three steps: 1) The appropriate physical balance laws are derived for m-phy- t cal quantities, ul""'~ with u = (ul' ... ,u ) and u(x,t) defined m for x = (xl""'~) E RN (N = 1,2, or 3), t > 0 and with the values m u(x,t) lying in an open subset, G, of R , the state space. The state space G arises because physical quantities such as the density or total energy should always be positive; thus the values of u are often con strained to an open set G. 2) The flux functions appearing in these balance laws are idealized through prescribed nonlinear functions, F.(u), mapping G into J j = 1, ..• ,N while source terms are defined by S(u,x,t) with S a given smooth function of these arguments with values in Rm. In parti- lar, the detailed microscopic effects of diffusion and dissipation are ignored. 3) A generalized version of the principle of virtual work is applied (see Antman [1]). The formal result of applying the three steps (1)-(3) is that the m physical quantities u define a weak solution of an m x m system of conservation laws, o I + N(Wt'u + r W ·F.(u) + W·S(u,x,t))dxdt (1.1) R xR j=l Xj J for all W E C~(RN x R+), W(x,t) E Rm.
A pioneer in the fields of statistics and probability theory, Richard von Mises (1883-1953) made notable advances in boundary-layer-flow theory and airfoil design. This text on compressible flow,...
Discover your next great read at BookLoop, Australia's trusted online bookstore offering a vast selection of titles across various genres and interests. Whether you're curious about what's trending or searching for graphic novels that captivate, thrilling crime and mystery fiction, or exhilarating action and adventure stories, our curated collections have something for every reader. Delve into imaginative fantasy worlds or explore the realms of science fiction that challenge the boundaries of reality.
Stay updated with the literary world by browsing our trending books, featuring the latest bestsellers and critically acclaimed works. Explore titles from popular brands like Minecraft, Pokemon, Star Wars, Bluey, Lonely Planet, ABIA award winners, Peppa Pig, and our specialized collection of ADHD books. At BookLoop, we are committed to providing a diverse and enriching reading experience for all.
Sign In
your cart
Your cart is empty
Menu
Search
PRE-SALES
If you have any questions before making a purchase chat with our online operators to get more information.
