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<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/628dde079ca87e087f5d34b1/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">目录<span class="ff2 sc1"> </span></div><div class="t m0 x1 h3 y2 ff1 fs1 fc1 sc1 ls0 ws0">用<span class="_ _0"> </span><span class="ff3 ls1">TTM<span class="_"> </span></span>方法生成翼型网格<span class="ff3"> <span class="_ _1"></span>...................................................................................................... <span class="_ _2"></span>3<span class="ff4 fs2"> </span></span></div><div class="t m0 x1 h3 y3 ff3 fs1 fc1 sc1 ls0 ws0">1.<span class="ff1">题目要求</span> <span class="_ _3"></span>................................................................................................................................. <span class="_ _2"></span>3<span class="ff4 fs2"> </span></div><div class="t m0 x1 h3 y4 ff3 fs1 fc1 sc1 ls0 ws0">2.<span class="ff1">解题思路</span> <span class="_ _3"></span>................................................................................................................................. <span class="_ _2"></span>5<span class="ff4 fs2"> </span></div><div class="t m0 x2 h3 y5 ff5 fs1 fc1 sc1 ls0 ws0">2.1 TTM<span class="_ _0"> </span><span class="ff1">方法介绍<span class="ff3"> <span class="_ _3"></span>............................................................................................................. <span class="_ _2"></span>5<span class="ff4 fs2"> </span></span></span></div><div class="t m0 x2 h3 y6 ff5 fs1 fc1 sc1 ls0 ws0">2.2<span class="_ _0"> </span><span class="ff1">控制方程<span class="ff3"> <span class="_ _3"></span>..................................................................................................................... <span class="_ _2"></span>7<span class="ff4 fs2"> </span></span></span></div><div class="t m0 x2 h3 y7 ff3 fs1 fc1 sc1 ls0 ws0">2.3 <span class="_"> </span><span class="ff1">差分格式</span> <span class="_ _3"></span>..................................................................................................................... <span class="_ _2"></span>7<span class="ff4 fs2"> </span></div><div class="t m0 x2 h3 y8 ff3 fs1 fc1 sc1 ls0 ws0">2.4<span class="_"> </span><span class="ff1">边界条件</span> <span class="_ _3"></span>...................................................................................................................... <span class="_ _2"></span>8<span class="ff4 fs2"> </span></div><div class="t m0 x2 h3 y9 ff3 fs1 fc1 sc1 ls0 ws0">2.5 <span class="_"> </span><span class="ff1">迭代方程</span> <span class="_ _3"></span>..................................................................................................................... <span class="_ _2"></span>9<span class="ff4 fs2"> </span></div><div class="t m0 x3 h3 ya ff3 fs1 fc1 sc1 ls0 ws0">2.5.1 <span class="_"> </span><span class="ff1">点<span class="_ _0"> </span></span>Gauss-Siedel<span class="_"> </span><span class="ff1">迭代</span> <span class="_ _4"></span>....................................................................................... <span class="_ _2"></span>9<span class="ff4 fs2"> </span></div><div class="t m0 x3 h3 yb ff3 fs1 fc1 sc1 ls0 ws0">2.5.2 <span class="_"> </span><span class="ff1">线<span class="_ _0"> </span></span>Gauss-Siedel<span class="_"> </span><span class="ff1">迭代</span> <span class="_ _4"></span>..................................................................................... <span class="_ _2"></span>10<span class="ff4 fs2"> </span></div><div class="t m0 x3 h3 yc ff3 fs1 fc1 sc1 ls0 ws0">2.5.3<span class="_"> </span><span class="ff1">点超松驰法（</span>PSOR<span class="ff1">）</span> <span class="_ _3"></span>................................................................................... <span class="_ _2"></span>10<span class="ff4 fs2"> </span></div><div class="t m0 x3 h3 yd ff3 fs1 fc1 sc1 ls0 ws0">2.5.4 <span class="_"> </span><span class="ff1">线超松弛法（</span>LSOR<span class="ff1">）</span> <span class="_ _2"></span>.................................................................................. <span class="_ _2"></span>11<span class="ff4 fs2"> </span></div><div class="t m0 x2 h3 ye ff3 fs1 fc1 sc1 ls0 ws0">2.6 <span class="_"> </span><span class="ff1">程序框图</span> <span class="_ _3"></span>................................................................................................................... <span class="_ _2"></span>11<span class="ff4 fs2"> </span></div><div class="t m0 x3 h3 yf ff3 fs1 fc1 sc1 ls0 ws0">2.6.1 <span class="_"> </span><span class="ff1">网格初始化</span> <span class="_ _3"></span>.................................................................................................... <span class="_ _2"></span>12<span class="ff4 fs2"> </span></div><div class="t m0 x3 h3 y10 ff3 fs1 fc1 sc1 ls0 ws0">2.6.2 <span class="_"> </span><span class="ff1">带入迭代方程</span> <span class="_ _3"></span>................................................................................................ <span class="_ _2"></span>12<span class="ff4 fs2"> </span></div><div class="t m0 x3 h3 y11 ff3 fs1 fc1 sc1 ls0 ws0">2.6.3 <span class="_"> </span><span class="ff1">引入边界条件</span> <span class="_ _3"></span>................................................................................................ <span class="_ _2"></span>13<span class="ff4 fs2"> </span></div><div class="t m0 x3 h3 y12 ff3 fs1 fc1 sc1 ls0 ws0">2.6.4 <span class="_"> </span><span class="ff1">判断是否收敛</span> <span class="_ _3"></span>................................................................................................ <span class="_ _2"></span>14<span class="ff4 fs2"> </span></div><div class="t m0 x3 h3 y13 ff3 fs1 fc1 sc1 ls0 ws0">2.6.5 <span class="_"> </span><span class="ff1">作收敛图</span> <span class="_ _3"></span>........................................................................................................ <span class="_ _2"></span>14<span class="ff4 fs2"> </span></div><div class="t m0 x1 h3 y14 ff3 fs1 fc1 sc1 ls0 ws0">3 <span class="_"> </span><span class="ff1">结果分析</span> <span class="_ _3"></span>.............................................................................................................................. <span class="_ _2"></span>15<span class="ff4 fs2"> </span></div><div class="t m0 x1 h3 y15 ff3 fs1 fc1 sc1 ls0 ws0">4 Matlab<span class="_"> </span><span class="ff1">程序</span> <span class="_ _2"></span>........................................................................................................................... <span class="_ _2"></span>19<span class="ff4 fs2"> </span></div><div class="t m0 x2 h3 y16 ff3 fs1 fc1 sc1 ls0 ws0">4.1<span class="_"> </span><span class="ff1">网格初始化程序</span> <span class="_ _3"></span>........................................................................................................ <span class="_ _2"></span>19<span class="ff4 fs2"> </span></div><div class="t m0 x2 h3 y17 ff3 fs1 fc1 sc1 ls0 ws0">4.2 <span class="_"> </span><span class="ff1">点高斯迭代法</span> <span class="_ _3"></span>........................................................................................................... <span class="_ _2"></span>20<span class="ff4 fs2"> </span></div><div class="t m0 x2 h3 y18 ff3 fs1 fc1 sc1 ls0 ws0">4.3 <span class="_"> </span><span class="ff1">线高斯迭代法</span> <span class="_ _3"></span>........................................................................................................... <span class="_ _2"></span>21<span class="ff4 fs2"> </span></div><div class="t m0 x2 h3 y19 ff3 fs1 fc1 sc1 ls0 ws0">4.4 <span class="_"> </span><span class="ff1">点超松弛迭代法</span> <span class="_ _3"></span>....................................................................................................... <span class="_ _2"></span>23<span class="ff4 fs2"> </span></div><div class="t m0 x2 h3 y1a ff3 fs1 fc1 sc1 ls0 ws0">4.5 <span class="_"> </span><span class="ff1">线超松弛迭代法</span> <span class="_ _3"></span>....................................................................................................... <span class="_ _2"></span>24<span class="ff4 fs2"> </span></div><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' 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<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/628dde079ca87e087f5d34b1/bg2.jpg"><div class="t m0 x2 h3 y1b ff3 fs1 fc1 sc1 ls0 ws0">4.6 <span class="_"> </span><span class="ff1">画图程序</span> <span class="_ _3"></span>................................................................................................................... <span class="_ _2"></span>26<span class="ff4 fs2"> </span></div><div class="t m0 x2 h3 y1c ff3 fs1 fc1 sc1 ls0 ws0">4.8 <span class="_"> </span><span class="ff1">追赶法求解三对角方程组</span> <span class="_ _3"></span>....................................................................................... <span class="_ _2"></span>27<span class="ff4 fs2"> </span></div><div class="t m0 x1 h3 y1d ff1 fs1 fc1 sc1 ls0 ws0">附录<span class="ff3"> <span class="_ _3"></span>.......................................................................................................................................... <span class="_ _2"></span>28<span class="ff4 fs2"> </span></span></div><div class="t m0 x1 h3 y1e ff1 fs1 fc1 sc1 ls0 ws0">感想<span class="ff3"> <span class="_ _3"></span>.......................................................................................................................................... <span class="_ _2"></span>29<span class="ff4 fs2"> </span></span></div><div class="t m0 x1 h3 y1f ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x1 h4 y20 ff2 fs3 fc1 sc1 ls0 ws0"> </div><div class="t m0 x1 h3 y21 ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x4 h4 y22 ff2 fs3 fc1 sc1 ls0 ws0"> </div><div class="t m0 x4 h4 y23 ff2 fs3 fc1 sc1 ls0 ws0"> </div><div class="t m0 x4 h4 y24 ff2 fs3 fc1 sc1 ls0 ws0"> </div><div class="t m0 x4 h4 y25 ff2 fs3 fc1 sc1 ls0 ws0"> </div><div class="t m0 x4 h4 y26 ff2 fs3 fc1 sc1 ls0 ws0"> </div><div class="t m0 x4 h4 y27 ff2 fs3 fc1 sc1 ls0 ws0"> </div><div class="t m0 x4 h4 y28 ff2 fs3 fc1 sc1 ls0 ws0"> </div><div class="t m0 x4 h4 y29 ff2 fs3 fc1 sc1 ls0 ws0"> </div><div class="t m0 x4 h4 y2a ff2 fs3 fc1 sc1 ls0 ws0"> </div><div class="t m0 x4 h4 y2b ff2 fs3 fc1 sc1 ls0 ws0"> </div><div class="t m0 x1 h4 y2c ff2 fs3 fc1 sc1 ls0 ws0"> </div><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a></div><div class="pi" data-data='{"ctm":[1.611792,0.000000,0.000000,1.611792,0.000000,0.000000]}'></div></div>
<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/628dde079ca87e087f5d34b1/bg3.jpg"><div class="t m0 x5 h5 y2d ff1 fs3 fc1 sc2 ls0 ws0">用<span class="_ _5"> </span><span class="ff2 sc1 ls2">TTM<span class="_ _5"> </span></span>方法生<span class="_ _6"></span>成翼<span class="_ _6"></span>型网<span class="_ _6"></span>格<span class="ff2 sc1"> </span></div><div class="t m0 x1 h6 y2e ff6 fs4 fc1 sc1 ls0 ws0">1.<span class="ff1 sc2">题目要<span class="_ _6"></span>求</span> </div><div class="t m0 x1 h3 y2f ff1 fs1 fc1 sc1 ls0 ws0">一、翼型几何形状<span class="ff3"> </span></div><div class="t m0 x2 h3 y30 ff1 fs1 fc1 sc1 ls0 ws0">如图所示，翼型的形状满足下列关系：<span class="ff3"> </span></div><div class="c x6 y31 w2 h7"><div class="t m2 x7 h8 y32 ff3 fs5 fc1 sc1 ls0 ws0">1</div><div class="t m2 x8 h8 y33 ff3 fs5 fc1 sc1 ls0 ws0">2<span class="_ _7"> </span>3<span class="_ _7"> </span>4</div><div class="t m2 x7 h8 y34 ff3 fs5 fc1 sc1 ls0 ws0">2</div><div class="t m2 x9 h9 y35 ff3 fs6 fc1 sc1 ls0 ws0">0.<span class="_ _8"></span>29<span class="_ _8"></span>6<span class="_ _8"></span>9<span class="_ _9"> </span>0.<span class="_ _8"></span>12<span class="_ _8"></span>6<span class="_ _8"></span>0<span class="_ _a"> </span>0.<span class="_ _8"></span>35<span class="_ _8"></span>1<span class="_ _8"></span>6<span class="_ _b"> </span>0.<span class="_ _8"></span>28<span class="_ _8"></span>4<span class="_ _8"></span>3<span class="_ _c"> </span>0.<span class="_ _8"></span>10<span class="_ _8"></span>1<span class="_ _8"></span>5<span class="_ _d"></span><span class="ff7">y<span class="_ _e"> </span>x<span class="_ _f"> </span>x<span class="_ _10"> </span>x<span class="_ _11"> </span>x<span class="_ _12"> </span>x<span class="_ _13"></span><span class="ff8"><span class="_ _14"> </span><span class="_ _15"> </span><span class="_ _16"> </span><span class="_ _17"> </span></span></span></div></div><div class="t m0 xa h3 y36 ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x2 ha y37 ff1 fs1 fc1 sc1 ls0 ws0">当</div><div class="c xb y38 w3 hb"><div class="t m3 xc hc y39 ff3 fs7 fc1 sc1 ls0 ws0">1<span class="_ _18"></span><span class="ff7">x<span class="_ _0"> </span><span class="ff8"></span></span></div></div><div class="t m0 xd h3 y37 ff3 fs1 fc1 sc1 ls0 ws0"> <span class="_"> </span><span class="ff1">时，取</span></div><div class="c xe y3a w4 hd"><div class="t m4 x9 he y3b ff3 fs8 fc1 sc1 ls0 ws0">0<span class="_ _19"></span><span class="ff7">y<span class="_ _1a"> </span><span class="ff8"></span></span></div></div><div class="t m0 xf h3 y37 ff3 fs1 fc1 sc1 ls0 ws0"> <span class="_"> </span><span class="ff1">（对称），弦长</span></div><div class="c x10 y38 w5 hb"><div class="t m5 x11 hc y39 ff3 fs7 fc1 sc1 ls0 ws0">1<span class="_ _8"></span>.0<span class="_ _1b"></span><span class="ff7">c<span class="_ _0"> </span><span class="ff8"></span></span></div></div><div class="t m0 x12 h3 y37 ff3 fs1 fc1 sc1 ls0 ws0"> <span class="_"> </span><span class="ff1">，</span> </div><div class="t m0 x2 ha y3c ff1 fs1 fc1 sc1 ls0 ws0">网格节点数可取</div><div class="c x13 y3d w6 hf"><div class="t m6 x14 h10 y3e ff3 fs9 fc1 sc1 ls0 ws0">3<span class="_ _8"></span>5<span class="_ _1c"></span>,<span class="_ _1d"> </span>2<span class="_ _8"></span>1<span class="_ _1e"></span><span class="ff7">I<span class="_ _8"></span>M<span class="_ _1f"> </span>J<span class="_ _8"></span>M<span class="_ _20"></span><span class="ff8 ls3"></span></span></div></div><div class="t m0 x15 h3 y3c ff3 fs1 fc1 sc1 ls0 ws0"> <span class="_"> </span><span class="ff1">（也可取得更密一些）</span> </div><div class="t m0 x2 ha y3f ff1 fs1 fc1 sc1 ls0 ws0">步长</div><div class="c x3 y40 w7 h11"><div class="t m7 x16 h12 y41 ff3 fsa fc1 sc1 ls0 ws0">1</div><div class="t m7 x17 h12 y42 ff3 fsa fc1 sc1 ls0 ws0">1</div><div class="t m7 x18 h12 y43 ff3 fsa fc1 sc1 ls0 ws0">2</div><div class="t m7 x19 h13 y44 ff7 fsa fc1 sc1 ls0 ws0">c</div><div class="t m7 x1a h13 y45 ff7 fsa fc1 sc1 ls0 ws0">x</div><div class="t m7 x1b h13 y41 ff7 fsa fc1 sc1 ls4 ws0">IM</div><div class="t m7 x1c h14 y45 ff8 fsa fc1 sc1 ls5 ws0"></div><div class="t m7 x1d h14 y41 ff8 fsa fc1 sc1 ls0 ws0"></div><div class="t m7 x1e h14 y42 ff8 fsa fc1 sc1 ls0 ws0"></div></div><div class="t m0 x1f h3 y3f ff3 fs1 fc1 sc1 ls0 ws0"> <span class="_"> </span><span class="ff1">，外边界半径取</span></div><div class="c x20 y46 w8 hb"><div class="t m8 x21 hc y39 ff3 fs7 fc1 sc1 ls0 ws0">2<span class="_ _8"></span>.5<span class="_ _21"></span><span class="ff7 ls6">Rc<span class="_ _22"></span><span class="ff8 ls0"></span></span></div></div><div class="t m0 x22 h3 y3f ff3 fs1 fc1 sc1 ls0 ws0"> <span class="_"> </span><span class="ff1">。</span> </div><div class="t m0 x23 h3 y47 ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x1 h3 y48 ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x1 h3 y49 ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x1 h3 y4a ff1 fs1 fc1 sc1 ls0 ws0">二、布置初始化网格<span class="ff3"> </span></div></div><div class="pi" data-data='{"ctm":[1.611792,0.000000,0.000000,1.611792,0.000000,0.000000]}'></div></div>
<div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/628dde079ca87e087f5d34b1/bg4.jpg"><div class="t m0 x2 ha y4b ff1 fs1 fc1 sc1 ls0 ws0">以弦长中点为网格外边界的圆心，从圆心作射线，射线之间的夹角</div><div class="c x24 y4c w9 h15"><div class="t m9 x25 h16 y4d ff3 fsb fc1 sc1 ls0 ws0">0</div><div class="t m9 x26 h17 y4e ff3 fsc fc1 sc1 ls0 ws0">2</div><div class="t m9 x27 h17 y4f ff3 fsc fc1 sc1 ls0 ws0">1<span class="_ _23"></span><span class="ff7 ls7">IM</span></div><div class="t ma x28 h18 y4e ff8 fsd fc1 sc1 ls0 ws0"></div><div class="t ma x29 h18 y50 ff8 fsd fc1 sc1 ls0 ws0"></div><div class="t m9 x2a h19 y50 ff8 fsc fc1 sc1 ls0 ws0"></div><div class="t m9 x2b h19 y4f ff8 fsc fc1 sc1 ls0 ws0"></div></div><div class="t m0 x2c h3 y4b ff3 fs1 fc1 sc1 ls0 ws0"> <span class="_"> </span>.</div><div class="t m0 x1 ha y51 ff1 fs1 fc1 sc1 ls0 ws0">射线与外边界的交点为</div><div class="c x2d y52 wa h1a"><div class="t mb x1a h1b y53 ff8 fse fc1 sc1 ls0 ws0"><span class="_ _24"> </span><span class="_ _25"> </span><span class="_ _24"> </span></div><div class="t mc x2e h1c y54 ff3 fsf fc1 sc1 ls0 ws0">,<span class="_ _26"> </span>,<span class="_ _25"> </span>,<span class="_ _27"></span><span class="ff7">x<span class="_ _28"> </span>i<span class="_ _29"> </span>J<span class="_ _8"></span>M<span class="_ _2a"> </span>y<span class="_ _28"> </span>i<span class="_ _29"> </span>JM</span></div></div><div class="t m0 x2f h3 y51 ff3 fs1 fc1 sc1 ls0 ws0"> <span class="_"> </span>. </div><div class="t m0 x1 h3 y55 ff1 fs1 fc1 sc1 ls0 ws0">三、迭代方法和收敛准则<span class="ff3"> </span></div><div class="t m0 x2 h3 y56 ff1 fs1 fc1 sc1 ls0 ws0">采用如下方法求解<span class="_ _0"> </span><span class="ff3">Laplace<span class="_"> </span></span>方程<span class="ff3"> </span></div><div class="t m0 xb h3 y57 ff1 fs1 fc1 sc1 ls0 ws0">（<span class="ff3">1</span>）<span class="ff5"> <span class="_ _2b"> </span></span>点<span class="_ _0"> </span><span class="ff3">Gauss-Siedel<span class="_"> </span></span>迭代；<span class="ff3"> </span></div><div class="t m0 xb h3 y58 ff1 fs1 fc1 sc1 ls0 ws0">（<span class="ff3">2</span>）<span class="ff5"> <span class="_ _2b"> </span></span>线<span class="_ _0"> </span><span class="ff3">Gauss-Siedel<span class="_"> </span></span>迭代；<span class="ff3"> </span></div><div class="t m0 xb h3 y59 ff1 fs1 fc1 sc1 ls0 ws0">（<span class="ff3">3</span>）<span class="ff5"> <span class="_ _2b"> </span></span>以上两种方法加超松弛；<span class="ff3"> </span></div><div class="t m0 x2 h3 y5a ff1 fs1 fc1 sc1 ls0 ws0">采用如下收敛准则：<span class="ff3"> </span></div><div class="c x30 y5b wb h1d"><div class="t md x31 h1e y5c ff8 fs10 fc1 sc1 ls0 ws0"><span class="_ _2c"> </span><span class="_ _2d"> </span><span class="_ _2e"> </span></div><div class="t me x32 h1f y5d ff3 fs11 fc1 sc1 ls8 ws0">11</div><div class="t me x33 h1f y5e ff3 fs11 fc1 sc1 ls0 ws0">,<span class="_ _2f"> </span>,<span class="_ _30"> </span>,<span class="_ _31"> </span>,</div><div class="t me x1c h20 y5f ff3 fs12 fc1 sc1 ls0 ws0">m<span class="_ _1c"></span>ax</div><div class="t me x34 h21 y5d ff7 fs11 fc1 sc1 ls0 ws0">k<span class="_ _32"> </span>k<span class="_ _33"> </span>k<span class="_ _34"> </span>k</div><div class="t me x35 h21 y5e ff7 fs11 fc1 sc1 ls0 ws0">i<span class="_ _35"> </span>j<span class="_ _c"> </span>i<span class="_ _35"> </span>j<span class="_ _36"> </span>i<span class="_ _35"> </span>j<span class="_ _b"> </span>i<span class="_ _5"> </span>j</div><div class="t me x36 h22 y5f ff7 fs12 fc1 sc1 ls0 ws0">A<span class="_ _8"></span>B<span class="_ _8"></span>S<span class="_ _37"> </span>x<span class="_ _38"> </span>x<span class="_ _39"> </span>A<span class="_ _8"></span>B<span class="_ _8"></span>S<span class="_ _3a"> </span>y<span class="_ _3b"> </span>y</div><div class="t me x1 h23 y5d ff8 fs11 fc1 sc1 ls9 ws0"></div><div class="t me x37 h24 y60 ff8 fs12 fc1 sc1 lsa ws0"></div><div class="t me x38 h24 y5f ff8 fs12 fc1 sc1 ls0 ws0"><span class="_ _38"> </span><span class="_ _3c"> </span></div><div class="t me x37 h24 y61 ff8 fs12 fc1 sc1 lsa ws0"></div></div><div class="t m0 x39 h3 y62 ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x1 h3 y63 ff1 fs1 fc1 sc1 ls0 ws0">四、作业要求<span class="ff3"> </span></div><div class="t m0 x1 h3 y64 ff1 fs1 fc1 sc1 ls0 ws0">写出：<span class="ff3"> </span></div><div class="t m0 x1 h3 y65 ff3 fs1 fc1 sc1 ls0 ws0">1<span class="ff1">，控制方程；</span>2<span class="ff1">，差分格式；</span>3<span class="ff1">，迭代方程；</span>4<span class="ff1">，程序框图；</span>5<span class="ff1">，结果分析</span> </div><div class="t m0 x1 h3 y66 ff1 fs1 fc1 sc1 ls0 ws0">附：<span class="ff3"> </span></div><div class="t m0 x1 h3 y67 ff3 fs1 fc1 sc1 lsb ws0">a)<span class="ff1 ls0">，初始网格图；<span class="ff3">b)</span>，最终收敛图；</span>c)<span class="ff1 ls0">，程序<span class="_ _6"></span><span class="ff3"> </span></span></div><div class="t m0 x1 h3 y68 ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x1 h3 y69 ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x1 h3 y6a ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x1 h3 y6b ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x1 h3 y6c ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x1 h3 y6d ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x1 h3 y6e ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x1 h3 y6f ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x1 h3 y70 ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x1 h3 y71 ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x1 h3 y72 ff3 fs1 fc1 sc1 ls0 ws0"> </div></div><div class="pi" data-data='{"ctm":[1.611792,0.000000,0.000000,1.611792,0.000000,0.000000]}'></div></div>
<div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/628dde079ca87e087f5d34b1/bg5.jpg"><div class="t m0 x1 h6 y73 ff6 fs4 fc1 sc1 ls0 ws0">2.<span class="ff1 sc2">解题思<span class="_ _6"></span>路</span> </div><div class="t m0 x1 h2 y74 ff5 fs0 fc1 sc2 lsc ws0">2.1 TTM<span class="_ _1a"> </span><span class="ff1 ls0">方法介绍<span class="ff5"> </span></span></div><div class="t m0 x2 ha y75 ff5 fs1 fc1 sc1 ls0 ws0">1974<span class="_ _0"> </span><span class="ff1">年，<span class="_ _4"></span><span class="ff5">Thompson<span class="ff1">、<span class="_ _3"></span><span class="ff5">Thames<span class="_ _0"> </span><span class="ff1">及<span class="_ _0"> </span></span>Martin<span class="_ _0"> </span><span class="ff1">系统而全面地完成了以求解椭圆型偏微分方</span></span></span></span></span></div><div class="t m0 x1 ha y76 ff1 fs1 fc1 sc1 ls0 ws0">程组为基础的贴体网格生成思想这方面的工作，故该方法称为<span class="_ _1a"> </span><span class="ff5">TTM<span class="_ _0"> </span></span>方法（<span class="ff5">TTM<span class="_ _0"> </span></span>系上述三</div><div class="t m0 x1 ha y77 ff1 fs1 fc1 sc1 ls0 ws0">人姓的首字母）<span class="_ _1c"></span>。<span class="_ _8"></span>用椭圆型方程生成的贴体网格质量很高，<span class="_ _1c"></span>而且计算时间增加不多，<span class="_ _1c"></span>不</div><div class="t m0 x1 ha y78 ff1 fs1 fc1 sc1 ls0 ws0">仅能处理二维、三维问题，而且还能处理定常和非定常问题，得到了广泛应用。<span class="ff5"> </span></div><div class="t m0 x2 ha y79 ff1 fs1 fc1 sc1 ls0 ws0">在数学上描述边值问题最简单的椭圆型方程就是<span class="_ _0"> </span><span class="ff5">Laplace<span class="_ _0"> </span></span>方程。</div><div class="t m0 x3a h3 y7a ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x3b ha y79 ff1 fs1 fc1 sc1 ls0 ws0">如下所示</div><div class="t m0 xa h3 y7a ff3 fs1 fc1 sc1 ls0 ws0">; </div><div class="c x3c y7b wc h25"><div class="t mf x3d h26 y7c ff3 fs13 fc1 sc1 lsd ws0">22</div><div class="t mf x21 h26 y7d ff3 fs13 fc1 sc1 lse ws0">22</div><div class="t mf x3d h26 y7e ff3 fs13 fc1 sc1 lsd ws0">22</div><div class="t mf x21 h26 y7f ff3 fs13 fc1 sc1 lse ws0">22</div><div class="t mf x3e h27 y80 ff3 fs14 fc1 sc1 ls0 ws0">0</div><div class="t mf x3e h27 y81 ff3 fs14 fc1 sc1 ls0 ws0">0</div><div class="t mf x2a h28 y82 ff7 fs14 fc1 sc1 lsf ws0">xy</div><div class="t mf x2a h28 y83 ff7 fs14 fc1 sc1 lsf ws0">xy</div><div class="t m10 xc h29 y84 ff8 fs15 fc1 sc1 ls10 ws0"></div><div class="t m10 xc h29 y85 ff8 fs15 fc1 sc1 ls11 ws0"></div><div class="t mf x1c h2a y86 ff8 fs14 fc1 sc1 ls0 ws0"></div><div class="t mf x1a h2a y84 ff8 fs14 fc1 sc1 ls12 ws0"></div><div class="t mf x14 h2a y80 ff8 fs14 fc1 sc1 ls13 ws0"></div><div class="t mf x1c h2a y87 ff8 fs14 fc1 sc1 ls0 ws0"></div><div class="t mf x1a h2a y82 ff8 fs14 fc1 sc1 ls14 ws0"></div><div class="t mf x1c h2a y88 ff8 fs14 fc1 sc1 ls0 ws0"></div><div class="t mf x1c h2a y89 ff8 fs14 fc1 sc1 ls0 ws0"></div><div class="t mf x1a h2a y85 ff8 fs14 fc1 sc1 ls12 ws0"></div><div class="t mf x1c h2a y8a ff8 fs14 fc1 sc1 ls0 ws0"></div><div class="t mf x14 h2a y81 ff8 fs14 fc1 sc1 ls13 ws0"></div><div class="t mf x1c h2a y8b ff8 fs14 fc1 sc1 ls0 ws0"></div><div class="t mf x1a h2a y83 ff8 fs14 fc1 sc1 ls14 ws0"></div><div class="t mf x1c h2a y8c ff8 fs14 fc1 sc1 ls0 ws0"></div></div><div class="t m0 x3f h2b y8d ff1 fs0 fc1 sc1 ls0 ws0">或写成<span class="ff3 ls15"> </span></div><div class="c x40 y8e wd h2c"><div class="t m11 x41 h2d y8f ff3 fs16 fc1 sc1 ls16 ws0">0</div><div class="t m11 x42 h2d y90 ff3 fs16 fc1 sc1 ls16 ws0">0</div><div class="t m11 x43 h2e y91 ff7 fs17 fc1 sc1 ls16 ws0">xx<span class="_ _3d"> </span>yy</div><div class="t m11 x2a h2e y92 ff7 fs17 fc1 sc1 ls16 ws0">xx<span class="_ _3e"> </span>yy</div><div class="t m12 x25 h2f y8f ff8 fs18 fc1 sc1 ls17 ws0"></div><div class="t m12 x44 h2f y90 ff8 fs18 fc1 sc1 ls18 ws0"></div><div class="t m11 x37 h30 y8f ff8 fs16 fc1 sc1 ls19 ws0"></div><div class="t m11 x1c h30 y93 ff8 fs16 fc1 sc1 ls0 ws0"></div><div class="t m11 x1c h30 y94 ff8 fs16 fc1 sc1 ls0 ws0"></div><div class="t m11 x1c h30 y95 ff8 fs16 fc1 sc1 ls0 ws0"></div><div class="t m11 x37 h30 y90 ff8 fs16 fc1 sc1 ls1a ws0"></div><div class="t m11 x1c h30 y96 ff8 fs16 fc1 sc1 ls0 ws0"></div><div class="t m11 x1c h30 y97 ff8 fs16 fc1 sc1 ls0 ws0"></div></div><div class="t m0 x45 h2b y8d ff3 fs0 fc1 sc1 ls0 ws0"> </div><div class="t m0 x38 h3 y98 ff1 fs1 fc1 sc1 ls0 ws0">将<span class="_ _5"> </span><span class="ff3">L<span class="_ _8"></span>aplace<span class="_ _1a"> </span><span class="ff1">方程的求解<span class="_ _6"></span>看成对一个导热系数为常数，无内热源，稳态的导热问题的温</span></span></div><div class="t m0 x1 ha y99 ff1 fs1 fc1 sc1 ls0 ws0">度场的求解，</div><div class="c x46 y9a we hd"><div class="t m13 x47 he y3b ff3 fs8 fc1 sc1 ls0 ws0">,</div><div class="t m14 x29 h31 y3b ff8 fs19 fc1 sc1 ls1b ws0"></div></div><div class="t m0 x48 h3 y99 ff1 fs1 fc1 sc1 ls0 ws0">表示温度，求出的解为矩形域中等温线叠加，如图<span class="_ _0"> </span><span class="ff3">1,2,3<span class="_"> </span></span>所示。<span class="ff3"> </span></div><div class="t m0 x38 h3 y9b ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x38 h3 y9c ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="t m0 x49 h3 y9d ff3 fs1 fc1 sc1 ls1c ws0"> <span class="_ _3f"> </span><span class="ls0"> </span></div><div class="t m0 x4a h32 y9e ff1 fs2 fc1 sc1 ls0 ws0">图<span class="_ _40"> </span><span class="ff3">1<span class="ls1d"> </span></span>等</div><div class="c x4b y9f wf hd"><div class="t m15 x0 h33 y3b ff8 fs1a fc1 sc1 ls0 ws0"></div></div><div class="t m0 x4c h32 y9e ff1 fs2 fc1 sc1 ls0 ws0">线<span class="ff3"> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_ _41"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_ _41"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_ _41"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span> <span class="_"> </span></span>图<span class="_ _40"> </span><span class="ff3">2 <span class="_"> </span> <span class="_"> </span></span>等</div><div class="c x4d y9f wf h34"><div class="t m16 x0 h35 ya0 ff8 fs1b fc1 sc1 ls0 ws0"></div></div><div class="t m0 x4e h32 y9e ff3 fs2 fc1 sc1 ls0 ws0"> <span class="_"> </span><span class="ff1">线</span> </div><div class="t m0 x38 h3 ya1 ff3 fs1 fc1 sc1 ls0 ws0"> </div><div class="c x4f ya2 w10 h36"><div class="t m0 x50 h37 ya3 ff1 fs2 fc1 sc1 ls0 ws0">等</div></div><div class="c x5 ya4 wf h38"><div class="t m17 x0 h39 ya5 ff8 fs1c fc1 sc1 ls0 ws0"></div></div><div class="c x4f ya2 w10 h36"><div class="t m0 x37 h32 ya3 ff1 fs2 fc1 sc1 ls0 ws0">线<span class="ff3"> </span></div><div class="t m0 x50 h3 ya6 ff3 fs1 fc1 sc1 ls0 ws0"><span class="fc2 sc1"> </span></div></div><div class="c x51 ya2 w11 h3a"><div class="t m0 x50 h37 ya7 ff1 fs2 fc1 sc1 ls0 ws0">等</div></div><div class="c x52 ya8 wf hb"><div class="t m18 x0 h3b ya9 ff8 fs1d fc1 sc1 ls0 ws0"></div></div><div class="c x51 ya2 w11 h3a"><div class="t m0 x37 h32 ya7 ff3 fs2 fc1 sc1 ls0 ws0"> <span class="_"> </span><span class="ff1">线</span> </div></div></div><div class="pi" data-data='{"ctm":[1.611792,0.000000,0.000000,1.611792,0.000000,0.000000]}'></div></div>
