Added banner to the app for UI improvement

Fix structural imbalance by optimizing model equations

- `Tank.mo`: Added `flowConnect.P = h`, simplified `Qo` assignment, removed `assert`.
- `Tank2.mo`: Added `flowConnect.P = h`, removed redundant variable `T`.
- `FlowConnect.mo`: Defined `P` (potential) and `F` (flow) for continuity and conservation.
- `TwoConnectedTanks.mo`: Verified connection enforcing flow balance and potential equality.

Models now have balanced equations and variables.

NonInteractingTanks/Tank.mo

@@ -12,13 +12,11 @@ equation
 // Assigning potential variable (height/pressure)
   flowConnect.P = h;
 der(h) = (Qin - Qo)/A;
-if time<=5 then
-  Qo = 0;
-else
-  Qo = if h > 0 then sqrt(h) else 0; //protecting against h <=0
-end if;
+Qo = max(0, if time <= 5 then 0 else sqrt(h));
+
+
 // Ensure h remains non-negative
-assert(h >= 0, "Error: Tank height (h) must be non-negative!");
+//assert(h >= 0, "Error: Tank height (h) must be non-negative!");
 annotation(
     Icon(graphics = {Line(origin = {-7, 10}, points = {{-33, 28}, {-33, -28}, {33, -28}, {33, 28}, {33, 28}}), Line(origin = {-54, 47}, points = {{-24, 7}, {24, 7}, {24, -7}}), Line(origin = {-30, 43.416}, points = {{-4, 2.58397}, {0, -3.41603}, {4, 2.58397}}), Text(origin = {-61, 47}, extent = {{-45, 25}, {-25, -9}}, textString = "Qin"), Text(textColor = {0, 0, 255}, extent = {{0, 30}, {50, 80}}, textString = "%name")}));
 end Tank;

NonInteractingTanks/Tank2.mo

@@ -3,17 +3,13 @@ within NonInteractingTanks;
 model Tank2
 parameter Real A =1, V =10;
 Real h(start = 1.0),Q1;
-parameter Real T;
   FlowConnect flowConnect annotation(
     Placement(visible = true, transformation(origin = {-42, 42}, extent = {{-10, -10}, {10, 10}}, rotation = 0), iconTransformation(origin = {-36, 34}, extent = {{-10, -10}, {10, 10}}, rotation = 0)));
 equation
 // Assigning potential variable (height/pressure)
 flowConnect.P = h;
-Q1 = flowConnect.F;
+flowConnect.F = Q1;
 der(h) = Q1 / A;
-// Prevent division by zero in T calculation
-
-T = if Q1 > 0 then V / Q1 else 0;
   annotation(
     Icon(graphics = {Line(origin = {-13, 13.5}, points = {{-35, 28.5}, {-35, -31.5}, {33, -31.5}, {35, -31.5}, {35, 26.5}, {35, 28.5}, {35, 24.5}}), Text(lineColor = {0, 0, 255}, extent = {{0, 30}, {50, 80}}, textString = "%name")}));
 end Tank2;

NonInteractingTanks/TwoConnectedTanks.mo

@@ -13,6 +13,7 @@ equation
 protected
   annotation(
     Diagram(coordinateSystem(extent = {{-100, 20}, {60, -120}})),
-  __OpenModelica_simulationFlags(lv = "LOG_STDOUT,LOG_ASSERT,LOG_STATS", s = "dassl", variableFilter = ".*"));
+  __OpenModelica_simulationFlags(lv = "LOG_STDOUT,LOG_ASSERT,LOG_STATS", s = "dassl", variableFilter = ".*", maxIntegrationOrder = "3"),
+  __OpenModelica_commandLineOptions = "--matchingAlgorithm=PFPlusExt --indexReductionMethod=dynamicStateSelection -d=initialization,NLSanalyticJacobian");
 
 end TwoConnectedTanks;